Please clarify the reference to Flash MX.
That was the name of version 6 back in 2002 (the first to incorporate video, but not well). It may not be enough, or if working with FLVs is possible at all it may be horrendously complicated (I'm sorry, I can't remember after all this time).
More recent Flash versions (8x) used a built-in FLV component (simply double-clicking an FLV wouldl launch an easy wizard). You make a "wrapper" SWF file of the correct dimensions, with extra space at the bottom if you want to load transport controls.
For multiple choice the "wrapper" SWFs can be loaded into an interface SWF as required using buttons (I generally use loadMovie into a placeholder movieClip).
Hope this helps.