I found that if you spawn the chicks over flowing water, they will swim when they fall into it. However, if you remove the water or spawn them on dry land and then add flowing water, it will run over them without them swimming upward, causing them to drown.
This has always been an issue in multiplayer, but has never been a major issue in single player until the implementation of the internal server. Since then, I have observed the issue happening even with lone animals, chickens especially.
Sebastiaan Chamberlain
I found that if you spawn the chicks over flowing water, they will swim when they fall into it. However, if you remove the water or spawn them on dry land and then add flowing water, it will run over them without them swimming upward, causing them to drown.