You can do that on many sites.
You'll need to advance past any cached section (or move back before the start of the last "click") before a new "part" appears in the FlashGot Media icon.
By jumping back & forth, you can get very close to the selection you'll want.
Not all (online) players allow advancing in this manner.
Not all video players will play back segmented/broken clips obtained in this manner.
And sometimes you can capture a segment, that would seem that it should be playable, but does not play in any case.
(Thinking, but can't recall with certainty, that you can do this not only with Flash, but mp4 & wmv too?)
Most often it works.
Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; rv:22.214.171.124) Gecko/20110420 SeaMonkey/2.0.14 Pinball NoScript FlashGot AdblockPlus
Mozilla/5.0 (Windows NT 5.1; rv:5.0) Gecko/20110626 Firefox/5.0 SeaMonkey/2.2