Connect Wall of Flags: Don't Embarrass Us

^{An entry in Fortnightly Topic Challenge #42: Wordless Connecting Walls}

K. G. (Knockoff Gladys) surprised me today with a note.

Hey, bobble!

I took your advice and made a puzzle. Who knew that was the way to get famous nowadays! You have to split these flags into 4 groups of 4. Then find another flag that fits into all of the categories – that’s where I’m going. Yes, yes, it’s dangerous to travel right now (and that’s important to remember!). But I’m going to do one of those virtual travel thingies. Anyways. I’ve attached the flag pictures. I’m sure you and those big-brained PSE folks will solve this in no time!

-K. G.

So, where is K. G. going on their "virtual travel thingy"? I may have said Puzzling was really good at this sort of thing. Don’t embarrass me us, solve this quick!