Tipicamente, Bladed Brush e Graça Cortante can't work together

The benefit of feat Bladed Brush, in part, says, "When empunhando a glaive, you can treat it as a one-handed piercing or slashing melee weapon… for all feats and class abilities that require such a weapon" (emphasis mine). The benefit of the feat Slashing Grace, in part, says, "Choose one kind of light or one-handed slashing weapon…." A creature that possesses the feat Bladed Brush only counts a glaive as a one-handed slashing weapon enquanto a criatura empunha a glaive; the glaive se remains a glaive, which is não a one-handed slashing weapon. No matter how an individual creature treats its glaive when that particular creature wields its glaive, the glaive is still an unsuitable weapon choice for the feat Slashing Grace.

Were Bladed Brush não to require actual empunhando, and, instead, its benefit started with You can treat a glaive as a one-handed piercing or slashing melee weapon…, it and the feat Slashing Grace would work fine together. Were the feat Slashing Grace não to mandate picking a specific kind of weapon, it and the feat Bladed Brush would work fine together. However, the feats both don't give an inch and remain incompatible.

While this GM can see that a few issues arise were either feat subject to a house rule changing it to fazer the two feats compatible—their interaction with the magohabilidade extraordinária spell combat springs to mind—, I imagine that because of the significant feat investment other styles of play would remain popular. I'd ask the player who pitched the house rule to show me his PC's plan first before I'd consider making such a house rule, though.

Making them work together anyway

To be extra clear, the feat Slashing Grace says, "Choose one tipo of light or one-handed slashing weapon" (emphasis mine). However, while this GM views a weapon's kind as the weapon em resumo—possessing only its printed statistics—, there's actually no formal definição de uma tipo of weapon. With that in mind, a GM that rules that the feat Bladed Brush alterar what kind of weapon a espada is while the creature wields a glaive gives creatures some options for gaining the feat Slashing Grace (glaive) if the creature's first taken the feat Bladed Brush.

For example, a human lutador that's already a worshiper of Shelyn (O Golarion deity of love and beauty) and that possesses the feats Arma Finesse e Foco da Arma (glaive) takes at level 1 the feat Bladed Brush. Then, at the end of the session wherein that human fighter gained enough experience points to advance to level 2, if that human fighter is wielding her glaive, she can take the feat Slashing Grace (glaive) as the feat Bladed Brush says that the glaive counts—while the feat's possessor empunha a glaive—"for for all feats… that require" a one-handed piercing or slashing melee weapon.

That is, while it's normalmente impossible to use the feat Bladed Brush to meet the prerequisite of the feat Slashing Grace (glaive), Avanço do Personagem says, "A character advances in level as soon as he earns enough experience points to do so—typically, this occurs at the end of a game session, when your GM hands out that session’s experience point awards." To do this then the character and the player must be aware that advancement is about to occur e the character must be at that session's end in a position to wield her glaive.

This is neither impossível nem particularly shady, Mas vontade typically be inesperado, certainly the kind of thing that should be discussed with the GM beforehand rather than suddenly sprung on the GM.

Likewise, a GM may allow a character like the aforementioned human fighter—if she's not in a position to wield her glaive upon advancing a level or if the GM nixes the character advancement scheme—to use the rules for Reciclagem to exchange another feat for Slashing Grace (glaive), although the GM may require the character to wield the glaive continuously for five days.

Observação: In addition to your Paizo messageboard threads from 2017, 2017e 2017, there're other threads about this interaction like these from 2016, 2017e 2017.

RAW: It is unclear ; Practically: yes

When you take the Slashing Grace feat you have to choose a "kind of light or one-handed slashing weapon", but Bladed Brush Combat only makes you able to use the glaive as a one-handed slashing weapon, it doesn't create a new "kind of one-handed slashing weapon". However it states that:

When wielding a glaive, you can treat it as a one-handed [...] slashing melee weapon [...] for all feats [...] that require such a weapon

So basically you could use your glaive for Piercing Grapple Combat for which there is no need to choose the weapon category to which it applies.

Does that mean you can choose "glaive" as the weapon category for Slashing Grace ? Not really if you stick to the rules-as-written. To work the formulation of Bladed Brush Combat should involve something like "you can choose glaives as a weapon category when a feat requires you to choose a one-handed or light piercing or slashing weapon".

Is this sentence intentionally missing? Probably not. Anyway there is no real problem with allowing the combination and as a DM I would accept that you choose "glaive" for your Slashing Grace if you already have Bladed Brush Combat. It just feels fair, not overpowered, and coherent in thematics.

Bladed Brush e Graça Cortante function together.

While the feats themselves do not directly tie together, we can display previously established concepts and rulings by the development team of Pathfinder to demonstrate that the temporarily-met prerequisite allow this combination to occur by RAI and RAW.

Aqui estão alguns exemplos.

A monk who can flurry can treat its BAB from monk levels as full and gain the full strength of Power Attack, allowing the character to benefit from this concept. This is in spite of it usually only flurrying for seconds per day:

How does a monk's improved BAB when flurrying interact with feats like Power Attack and Combat Expertise, which have different effects depending on your BAB?

The monk uses his improved flurrying BAB to determine the effect of those feats.

Another example would be that a brawler in the midst of using his brawler's flurry is considered to possess different abilities while using his class ability, and could take feats that need those requirements met:

A brawler can use the feats granted by brawler's flurry to qualify for other feats, but can only use those other feats when using brawler's flurry (as that's the only time she actually meets those prerequisites).

To further add to the idea of selecting feats in temporary situations, but needing prerequisites active to use them, here is SKR describing putting on an item to meet a feat prerequisite:

Are you wearing the item? Do you therefore have the prerequisite? Then you can select the feat. But if the prereq goes away, you can't use the feat.

The 'toggling' of a feat back on is even supported in the core rules:

A character can't use a feat if he loses a prerequisite, but he does not lose the feat itself. If, at a later time, he regains the lost prerequisite, he immediately regains full use of the feat that prerequisite enables.

Another example is how you cannot meet the prerequisites for Foco da Arma while you are not proficient with a weapon, yet a shifter can take Weapon Focus (Claws).

There is even a catch-all rule thrown around by the devs that you can always lock in a prerequisite as viable if you can keep the bonus going for 24 hours, which you can do by just holding your glaive.

While holding the glaive, you treat the weapon as a one-handed slashing weapon for the purpose of feats. You train with the glaive using Bladed Brush to develop the skills of Slashing Grace. When you aren't holding a glaive with Bladed Brush active, you lose the ability to use Slashing Grace.

Learning Slashing Grace in this way effectively makes Bladed Brush a prerequisite feat, so if you ever lose access to Bladed Brush for any reason, you would lose Slashing Grace.

tl;dr Yes they do, but you lose Slashing Grace if you lose Bladed Brush.

Bladed Brush specifically DOES works with Slashing Grace, based on this quote from Bladed Brush (emphasis added):

treat it as a one-handed piercing or slashing melee weapon and as if you were not making attacks with your off-hand for all feats and class abilities

Because of this, you are treating Glaives as a one-handed weapon for all intents and purposes. Importantly, you devo have Bladed Brush before you get Slashing Grace, as Glaives are not a valid choice for Slashing Grace until after you have Bladed Brush.

There are numerous ways (1 Fencing Grace Feat) (2 SwB Precise Strike Deed) that Paizo has phrased it, and this is one of the more clunky, but all of the Q & A's seem to agree that Feats and abilities that work toward a 'one-handed' DEX build are intended to work together.