Let’s say I became best buddies with a Kyogre. I then traded it to a friend, and then traded for it back. Would I still be best buddies with it, or would it start over?
Last I checked you can't trade a single Pokemon more than once in GO, so you wouldn't be able to get it via trade back. As for it's friendship being reset, whenever you go to trade a Pokemon there is a very specific and obvious message in game stating that the Pokemon's friendship will be reset.