Well, there are a lot of different ways to get from point A to point B with this question. You could buy Flash CS4 and use a component. Or you could buy a pre-built video player, which is probably the best option.
For example, this player is very popular (and flexible) and will work directly with your MP4 content:
I'm using Flash CS4 and it comes with "Adobe Media Encorder"
with the encorder, I convert MPEG and MOV to FLV.
the encorder is very simple, but I'm happy with it.