Your old flasher is a 2prong and the light fixtures themselves had the ground. BLACK brought power to the flasher from the key, GREY carried it to the switch. Switch passed it to BLUE or ORANGE, etc...
With that M-Flash, it needs to sit in between BLACK and GREY because BLK brings the power to the flasher, GREY onto the switch... You’ll have to tie RED/BLK /GREY together, then tie M-Flash BLK to ground. That should basically “replicate” the stock circuit with a newer flasher type.
You can damage a battery by reversing polarity, but not by doing so with that flasher. Jumper cables, sure, but not your “accident”. More likely you’ve damaged a switch or connection somewhere, OR, cooked the fuse block and you don’t realize it.