Video issues like this can be very tricky to figure out.
It happens on both youtube and facebook? You need to find out if others are seeing the symptoms. Post a link to the youtube video (I’m off facebook so if it’s not public without having to register I can’t get to it there).
If it is just you seeing the problem a quick step to do since you suspect Flash player (after checking you have latest version) is to turn off video acceleration in the player to rule out a problem with your card or drivers. Yeah a longshot but an easy step in the process of elimination.
Does the issue occur at the same place in the video or at any place when you switch to fullscreen? Does it happen only in fullscreen? Will it work at all in fullscreen (even after restarting or jumping ahead in the vid)?
Are there any glitches or stutters or anything not perfect in the source video? Small glitches can cause big issues down the line (some players OK with it some not). Also, video sites transcode your video so borderline encoding problems can be magnified there as well.
Post a link to the youtube video.