Todas as velocidades serão reduzidas para 0.
Especificamente, você não pode voar quando sua velocidade é 0:
PHB p. 191
Flying Movement
If a flying creature is knocked prone, has its speed reduced to 0, or is otherwise deprived of the ability to move, the creature falls, unless it has the ability to hover or it is being held aloft by magic, such as by the fly spell.
Quanto a outros tipos diversos de movimento, eles também dependem da velocidade:
PHB p. 182
Special Types of Movement
Movement through dangerous dungeons or wilderness areas often involves more than simply walking. Adventurers might have to climb, crawl, swim, or jump to get where they need to go.
Climbing, Swimming, and Crawling
While climbing or swimming, each foot of movement costs 1 extra foot (2 extra feet in difficult terrain), unless a creature has a climbing or swimming speed. At the GM’s option, climbing a slippery vertical surface or one with few handholds requires a successful Strength (Athletics) check. Similarly, gaining any distance in rough water might require a successful Strength (Athletics) check.
Já que estes dependem do movimento, se você não pode se mover porque sua velocidade é 0, você não pode pré-forma-los.
Em geral, todas as suas velocidades estão conectadas e quando você usa parte de sua velocidade para um tipo de movimento, subtrai-a de todas. O PHB tem um bom exemplo disso:
PHB p. 190
Using Different Speeds
If you have more than one speed, such as your walking speed and a flying speed, you can switch back and forth between your speeds during your move. Whenever you switch, subtract the distance you've already moved from the new speed. The result determines how much farther you can move. If the result is 0 or less, you can’t use the new speed during the current move.
For example, if you have a speed of 30 and a flying speed of 60 because a wizard cast the fly spell on you, you could fly 20 feet, then walk 10 feet, and then leap into the air to fly 30 feet more.