A 3DS will need a capture board installed onto the console, and a GBA can be captured with a GameBoy Player attachment for a GameCube. Then you can build a setup with a capture card and software like OBS. Without either of those, your only option is to record the screens of the consoles with your phone, and edit in a timer in post with video editing software and timer software like LiveSplit.
GBA games can also be captured with a DS capture card, and of course you could use Wii U virtual console for some games.
I thought a 3DS didn't have the GBA slot on it like an original DS did. I could be thinking of something else though, or like a specific type of 3DS.
Yes but why are you talking about a DS when OP has and is asking about a 3DS? Capture boards for a DS and a 3DS are different, so it’s probably best not to confuse anyone by talking about a different console.
Because you can’t capture a GBA SP, I was suggesting another option for capturing GBA games. Just like how you brought up the Game Boy Player, even though the OP didn’t mention GameCube.