I'm sorry about your tire misfortune. This reminded me of the flat tire saga I had with my 2014 i3 about 3 years ago. I was driving to work in the morning in the left lane, rounding a curve in the freeway, when I saw the mangled ladder laying across the lane I was in. I had nowhere to go and no time to stop so I ran over it with both driver side tires. I heard a bang, I emitted an expletive and quickly menued to the tire pressure screen where I saw that the left rear tire was losing air pressure so I pulled on to the left shoulder of the freeway wishing I had a spare tire. When I got out of the car, the left rear was flat.
I debated using the repair kit then and there when a SacMetro FSP (Freeway Service Patrol) tow truck pulled over behind me. He gave me a brochure which said "A free emergency road service for Sacramento area commuters". I was in luck. The service would provide me a tow to the next freeway exit and I'd be on my own after that, but at least not on the freeway. He loaded up my car and drove it to the next exit and unloaded it on an empty frontage road so at least I was safe.
Now I decided to get the repair kit out of the frunk and squirt the expensive repair juice into my back tire according to the directions. It kept flowing out of the hole so it did not appear to be working. See photos here: https://photos.app.goo.gl/ttwGGHbXJXkqdTaG9
I waited and tried to put some air into the tire but it would not hold any. I waited longer. Still would not hold air. What to do? I wanted to be towed to a tire repair place (Costco actually since I had bought these tires new about 2 weeks before and they warrantee them) so I used the emergency call button in the upper console to contact BMW. I was told that they would only tow me to a dealer. I wasn't happy about this because I figured I'd get reamed but I went along with this.
Eventually a tow truck showed up and carried the car to the nearest BMW dealer. I was about to go in, annoyed that I had recently bought new tires and the dealer will likely charge a lot more than Costco but I decided to look at the tire again and it wasn't completely flat meaning that it was holding some air after a couple of hours of the juice stewing around inside. I filled the tire to a reasonable pressure and it held! Screw the dealer I thought, I'll drive slowly to the nearest Costco while monitoring the air pressure on the screen. And I made it!
However, Costco said they couldn't fix it, I can't remember exactly why, maybe it was because of the repair juice in the tire. Great. So my next step was to refill it with air and hope I could make it home about 15 miles away. I could always stop and refill along the way as long as it could hold some air as it was slowly leaking down but I finally made it home. Now I could remove the wheel and take it to the Costco I'd originally bought it from and get it fixed. So when I got home, I took off the wheel and drove it to Costco. They said the tire was too damaged to be fixed so I'd need a new one. They could not find one anywhere in their supplier stock. Ha Ha! I have to say that the guys at Costco were really helpful as they allowed me to use their computer to check Tire Rack stock which actually had one of these bad boys. Eureka! Costco could not order the tire directly from Tire Rack so I ordered and paid for it and it arrived at my home the next day and I drove it up to Costco. They said they would reimburse me for the cost of the tire (which they did) to honor their warrantee.
I never thought about the TPMS and I don't think it was replaced and it still works fine. I could hardly believe this whole episode only cost mer a replacement BMW tire repair juice container, other than the wasted day of course, so I was lucky unlike HuggyBeard. It was quite an adventure greatly lengthened by not carrying a spare!
The moral of this story: Don't get a flat tire in an i3!!!!!!!!