When I tap a video to play on YouTube in Firefox Mobile, it launches in the YouTube app instead of playing in the page. Is that what you're getting?

When I launch the same video from the stock browser, it plays in a full screen player (I'm not sure whether it is part of the browser or some other app).

The mobile Firefox 14.0 does support Flash if you are using Android 2 or 4 (does not work on Android 3). Also if the device has a Tegra 2 cpu, there is a known conflict preventing Flash from working.

What is your phone/tablet model specifically as that would help to answer why Flash is not working.

Solved! Downloaded YT app and NOW FF does play YT