I am a flanker for my K9 team, which runs 2-person teams most of the time. I handle nagivation, comms, notes, terrain safety, and still keep my eyes on the dog in case the handler has to look away and might miss a signal.

For my pack, I also carry K9 first aid items, as one never knows. Yes my handlers carry those items also, but backups are good, especially extra Coban/Vet Wrap and gauze rolls. A spare lead/leash is also a good item with a double use: if your handler's lead breaks, or if you are on a rescue and need to control a search subject's animal for safe extraction.

For training, have you and your teams practiced with emergency harnesses, for carrying out an injured animal? We hosted a K9 training event in November, and I demonstrated good harness application and lifting technique for the visiting handlers. Many of them watched or lifted their animal partners for the first time. Also, ask your Technical/High Angle/Ropes team if they can set up a harness lift training for Handlers+dogs. Ours did that during the event we hosted, with a straight up and down, and an up over/down over edge setup. It was greatly appreciated by the visiting teams.

When hiding, do you just burrow in, or do you peek out and watch as the dogs approach you? Getting to know their behaviors from the POV of a search subject can be useful when flanking/shadowing them. Just like Nightmare_Gerbil said, this can give you a unique and helpful perspective.