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While there are third party applications that can handle flash, I don't have any experience with them. The "real deal" is Macromedia Flash [macromedia.com] but it's also the most expensive.
Is there a particular reason why you aren't posting the movie as a actual movie file format, such as Quicktime or WMV?
I have a digital video recorder card [miglia.com] for my machine that allows me to plug in any RCA, S-Video, or even Cable source into the back and I record the video using the software that came with it. You can also accomplish this with firewire or USB devices [miglia.com] that have a "video in" that matches the "video out" from your VCR, DVD player, or digital camcorder.
There are also companies out there that will take your video tapes and give you back a CD or DVD with the encoded movie in whatever format you want. This should be cheaper and easier than buying the hardware and learning it yourself unless this will be an ongoing need.