How many Flash files?
How big will they be?
Do you have any idea how popular they might be?
If you can let us know a bit more I'm sure you can get some really good recommendations. It all, after all, depends on what scale you're talking about. I mean, YouTube theoretically could be described as hosting "some online flash videos"
I think if your traffic only 10-20 visits per day then you can use shared hosting at first.
After your first 3 months and the traffic is growing then you can move on to VPS with ffmpeg supports.
This is to reduce cost so you can focus the fund on your website's marketing with Yahoo or Google.