Been playing through the GOG version of SS:FE this week and accidentally hit F7 and I noticed the screen said recording. I let it record until I had killed all and then turned F7 off. Now I'd like to play back the recording but have no clue where the game saves the recordings it makes. If anyone knows please let me know. Thanks.

I don't believe you can view the demos the game records outside of the game itself since they aren't technically videos but rather are raw gameplay captures. Then again, it's something I never bothered with personally.

As to the location, check the game install directory for a folder with "Demos" in its name.