I've been an EMT for 26+ years and was a volunteer fireman for 21 of those years. I didn't know about the BK3 back then or I would have carried it.
Instead, I carried a pair of the leather handled Kabar 3/4 shorties in a leather sheaths. In Texas, I didn't have to worry about the open/concealed dilemma, so I COULD have carried them in my bunker coat pockets, but as I had been a SCUBA diver since 1975 and carried my dive knives attached to my backpack harness, I strapped my shorties to the SCBA harness.
Since we only had 13 guys who ran nearly every call the department had, we essentially had SCBAs personally assigned for use (I had JSCBA08 - Jonestown SCBA #08). Didn't matter as after I started carrying that way, everyone else did as well.
There's a couple of ways that you could mount a pair on your SCBA harness when on duty (I'm assuming you're paid and on a 24/48 schedule).
And why 2? Well, if you get tangled up (like you did) you may not be able to reach a knife on your right side with your left hand.
I dosed up the leather handles and sheaths liberally with Obenauf's. That protected them fairly well from water. They were cheap enough that if they got scorched a bit, they were cheap enough to replace. I really really tried not to get scorched.

The chief frowned on it.