I was playing a game last night, and here's a move I pulled off. It was totally casual, so he let me do it even though he wasn't sure(plus, I let him bounce a Power Gem a couple minutes late when he realized he forgot).

1. Flip Brother I Satellite
2. Chain Ahmed activation
3. KO Brother I Satellite, search deck for Checkmate Safehouse
4. Flip Checkmate Safehouse, calling Checkmate and Team X
5. Resolve Brother I Satellite, and search deck for Team X character

Does this work? Can I do this to search my deck for a non-Checkmate character, if when Brother I Satellite resolves they're teamed up?

It's fine. You put the initial Brother I Satellite's effect on the chain when you flip it (The effect is independent of the location itself. When you KO the location, the effect is still on the chain). By the time its effect resolves, you are teamed up, so you search for a Checkmate character or a Team X charater. The chain is beautiful. You can pull all sorts of shenanigans with it.

When you flip up Brother I satellite, its effect goes on the chain just like anything else. So yes you can respond to flipping it up, by then using Ahmed and Koing it to get a Checkmate Safehouse. After Ahmed's ability resolves you can flip the Safehouse still before the Brother I resolves, crossing over the teams. Since you are teamed up at that point you can grab a char. from either team. Just remember that all effects are put on the chain before resolving. :)

as long as you controled "team X' when you flipped the Safehouse, that was a perfectly legal sequence of events.

Awesome. I felt so cool when I came up with that on the fly.