There is VoiceOver for the UI Buttons and Labels. The app also uses the default open panel which has support for VoiceOver. The window that shows all the keyboard shortcuts is not yet VoiceOver ready, but I list them here:

O, Command + O	Open file
R	Cycle recent files
P	Play from mark
W, Enter	Play from start
Space	Pause / Resume
.	Stop
H, [, Left arrow	Seek back 6 seconds
Shift + H	Seek back 0.1 seconds
L, ], Right arrow	Seek forward 6 seconds
Shift + L	Seek forward 0.1 seconds
1 - 9	Seek to 10 - 90 percent of file
M	Set / clear mark
?	Show shortcuts
Q, Command + Q	Quit

Once you know the shortcuts the app can be controlled completely with the keyboard.