Regarding the selection between HTML and Flash; that is entirely up to YouTube I'm afraid. For iOS the WP YouTube Lyte just uses the default YouTube iframe embed code. Inside that iframe, YouTube will, depending on a number of factors, display the Flash or HTML-version.
Last time I tested (which is, I have to be honest, over half a year ago) this worked. This probably also depends on the availability of the YouTube app in iOS, which isn't there by default any more?
Some questions maybe to help me understand:
- Do you have the YouTube app installed?
- Do other YouTube embeds work (e.g. this oembed-based embed on my testblog)?
- what happens? do you see the thumbnail and/or a play-button? can you click play? what do you see?