Flash is not a requirement in any part of the site.
The "lightbox" popups have issues on mobile browsers, but otherwise it makes no difference if you use ios/android/wp or something else as we are using fully standard code here. But in essence the phone screens are too small, and aome tablet is the minimum in my mind for any meaningful usage.
The mobile usability is one of the to-do items. I wish aws to be a cross-platform application, properly..
(ps. Windows Mobile kicks ass over Android any day and is fully par with iOS too (some more smarter things integrated too), check in autumn when the WP8 comes available.. Been using a Nokia Lumia 800 for past 6 months)