Hey there.
You can, in fact, use a mouse & keyboard with an Android Phone. There's methods both by USB hub and with specialised keyboards - I have a friend who used to mess around with that a lot.
Puffin is a terrific mobile flash browser.
But it may be easier (and possibly cheaper) to simply buy a Chromebook. Chromebooks should be able to run BD perfectly well, considering Google Chrome has Flash built right in. They have a keyboard, a touchpad (plus you can of course add a mouse) and you can get them for about 200$. Cheaper then buying a new mobile and allows you to get an LED that doesn't support On The Go (assuming that is some form of new technology, you can get terrific PC screens for much cheaper prices).
See this link concerning
chromebooks.
I'll have to look into On The Go, but you should be able to use an existing mouse & keyboard with your android device using only a special hub. I'll get you some more information on this after contacting my friend.