That’s a great question. My comments will be based on my experience with Anki Droid. Full disclosure: I am not blind.
With the correct settings, I believe you can configure Anki Droid for a fairly accessible experience.
Audio can be generated ahead of time on desktop before syncing your cards to Anki Droid with the Awesome TTS add-on. Anki Droid can also do text-to-speech on the fly. I would recommend getting a blue tooth controller to go through reviews. Or you can configure Anki Droid to allow controlling it with gestures like swiping left, right, up, down, shaking, etc. rather than pressing specific areas on the screen. Gestures might be easier because it won’t require any additional configuration with a 3rd party app, which is necessary to map buttons from the bluetooth controller to the correct key strokes.