I doubt it's a codec conflict since I have only one codec pack installed. I've used the Codec Tweak Tool several times but it didn't really do anything. I just downloaded GOMPlayer and it does play FLV files fine, but I'm not very fond of the layout. The player covers a big area of the screen even when playing audio files. I resized the window but it's still rather large, especially compared to BSPlayer which is very compact.
That said, I just reinstalled K-Lite Codec Pack and now FLV files work absolutely fine in BSPlayer again. I do remember this happening before though, and the problem would return after a few weeks. It's ridiculous, I know, I have no idea why it works this way too. Maybe someone could clue me on any possible reasons for its occurrence?
Right now, I'll stick with BSPlayer since I'm especially of its skinnable nature and user-friendliness. Thanks for all the help, I appreciate it.