The results of the above will almost certianly not be properly playable on the XO. Especially if you try to play it with Adobe's Flash player it is a resource hog and far to heavy for the XO. Your best bet is to convert the .flv file to a .oga (ogg/theora) video that the XO can play natively. There is a fast, easy, open source program called oggconvert that does this nicely.. you can convert a bunch and throw them and a thumbdrive and they'll be click to watch.. (The XO doesn't have to power to handle high def or high framerates so depending on the video you might want to run it through something like avidemux (another open source program for dealing with videos). You'll need to run oggconvert and avidemux on you main Desktop/laptop but you'll be able to make XO friendly videos quickly once you get the routime down.
There is also an XO friendly portal at http://olpc.dailymotion.com/
Which works on the XO out of the box. (no mucking about installing flash, etc)
Short of something like the above portal the answer is basically "NO the XO can not handle flash Video" even ubuntu on the XO has to download and convert the video and then play it in a non "adobe flash" player. It is simply a case of lack of horse power (on the XO side) and terrible use of resources (on the Flash side). That aside the XO is very capable of playing very watchable, in sync, fullscreen videos.
I watch the evening news (that I convert from a web) and many other videos on my XO so if anyone wants pointers feel free to ask.
Hope this helps