First, figure out why you had problems getting out of your pedals. They might need adjustment, the cleats might need to be adjusted or replaced, etc. If you are just new to clipless pedals, even more important to check those things - a bike shop can do that for you. That is probably the most important thing of all.

You didn't detail what kind of flat - lots you can do to minimize flats. On a long, steep downhill years ago where I had to ride the rim brakes on my old bike (I weigh 230 lbs), I had a flat because the rims heated up tremendously and the tube area around the valve melted. That taught me about pulsing the brakes to allow some cooling, etc. (It also caused me to go with disc brakes on my new road bike.)

If it was a flat because you hit or ran over something on the downhill, sometimes that is unavoidable, many times it is avoidable if you go slower. I tore my rotator cuff (not because of cycling) and had surgery on it 5 years ago and now I try to minimize the chances of falling at high speeds and going through that again. So, I'm much slower going downhill than I used to be. Around here, potholes and animals running across the downhilll are constants.

I've found most of my flats are actually caused by something I picked up on a tire on the previous ride. After each ride, I check both tires by rotating the wheel one turn and looking/feeling for anything stuck in the tire. If you find anything, let the air out and remove the offender with tweezers or needle nosed pliers and check to see how deep it went - further action may be required.

My new bike is tubeless-ready, I haven't gone that way because I don't get flats that often, but that's another option if your wheels support it.

The part about the car: it sounds like if you could have gotten your feet out of the pedals, you could have stopped on the side and the car would have gone by you. As others said, the driver would have no way of telling you had a flat.

After many years of pooh-poohing a rear view mirror on my bike, I put a bar end mirror on and now am able to always know if a car is behind me and what it is doing. The mirror didn't replace looking backwards, but it has greatly improved my situational awareness (we cybersecurity geeks love that term...) so that when a squirrel or groundhog runs out when I'm going downhill, I know if swerving left is a worse option than swerving right into the ditch...

There are roads I don't bike on because there are downhills with low visibility, no shoulders and high speed/high levels of traffic - if that was the case, avoid that stretch of road. If there is no alternative, Then, all of the above can help make that stretch less dangerous for you - all things you can do, vs. hope the driver behind you does!