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I got to the same place as Steam users have described as "Beak beak flying bug".
In second tower, after Beak Beak has to eat the flying pill from the bowl, I click him and he starts flying, but he can't move anywhere, including up.
We managed to get the flying dog down!

First: Save your game (in a new slot).
Load the newly saved game. Beak Beak will now be on the ground again (on the ledge).

Strange things might happen (see attached image), but just keep reloading the game and try agian, until you get away with BreakBeak.
Thanks for answering your own question. With you being the top google search result it really saved me a lot of time.
Just read the reviews and the game is still broken after 2 years? ( sighes)
some developers ..... :D

Its funny to see devs having problem getting their own game code right, almosts as if the gamecode was left by an alien ancestor and the dev is struggling to decipher the ancient code use when the game was written eons ago , it seems to be a common problem nowadays cause Steam has dozens of gamedevs that have a hardtime getting their code right aswell.

Yes, this scene is still buggy.
The save/load workaround didn't work for me, though. It created another bug, Tom appearing in the scene, standing in the air. The "special vision" was gone.

Avoiding the bug: After picking up the lever in the tunnel, click on the kraken, watch cut-scene, pick up button that drops.
Then, IMPORTANT!, click ABOVE the dog to make him fly up, then click bottom leftin the scene to make him descend.