I think you want to kick well inside your flexibility.
I have a routine I used to do a lot that gave me the ability to kick cold. Sometimes I can't touch my toes because of my inflexibility and previous back injuries, but I can wake up at 3am and kick to the head without stretching thanks to this drill.
Besides normal kicking flexibility drills that I'm sure you know, sometimes back pain with kicking is rooted in another part of the body. You can also have a weakness that is aggravated by incorrect exercises.
Muscles in the lower back are designed for stability rather than motion. Any low back exercises where you arch the back, especially while holding a weight, isn't terribly useful. Dead lifts and rows are good because you keep the back straight while bending forward while holding a weight and coming up from the waist isn't that useful. Are you doing any odd back exercises that aren't stability, but instead dynamic motions with weights?
There could also be a weakness in your abs and your back is compensating. Bridging exercises are great for this. Find bridges that activate your abdominal muscles below your belly button to start. See if you are bad at any abdominal exercises and work on those.
Try to stay away from situps. Most people shouldn't do them. They lead to increased hip tightness. Look for things like knee ups or reverse crunches.
Some of my back pain was due to weak glutes, and when I started to do exercises for my butt and hamstrings, it improved dramatically.
Everything I mentioned - proper low back exercise, less situps, more bridges, flexibility, the kicking drills I can post later for you if you want, glute and hamstring strengthening, and so on, all that can be good for almost everyone.
