There are some abilities like Sentinel which let you reduce a creature's speed to 0.
If a creature with any kind of other speed, like climbing-, flying- or swimming speed can it use these to move, or are all speeds reduced to 0?
For example, a Dragon, which is moving out of melee range gets hit by someone's opportunity attack and has its speed reduced to 0. Can it still fly?
Best Answer
All speeds will be reduced to 0.
Specifically you cannot fly when your speed is 0:
PHB p. 191
As for other miscellaneous types of movement, they also depend on speed:
PHB p. 182
Since these depend on movement, if you can't move because your speed is 0 you cannot preform them.
In general, all of your speeds are connected and when you use part of your speed for one type of movement, it subtracts it from all. The PHB has a good example of this:
PHB p. 190