ok, I don't mean to sound patronizing, but this actually works.
I used to tell my preteam kiddos this:
Pretend that you have some bird food on your toes. Now, kick up to a handstand, and push all the way to the ceiling so you can feed the baby birds just above your toes. Make sure you push tall enough, because those little birdies are hungry.
Sometimes a silly visual is the best thing....!
The pic isn't showing up, but I'm going to guess you have the two problems that most people have with archy handstands.
Problem #1, the first that needs to be fixed, is most likely not in the back -- it's in the shoulders. If the shoulders are not fully extended, the back will be arched 99% of the time, and it is generally inneffective to try to fix the back without fixing the shoulders. The best way I've found to work on this is to practice the position while standing on your feet. Arms by your ears, tight tall body just like a handstand, back very slightly hollowed. Now, without allowing your back to arch, try to open your shoulders more, pushing your fingertips back towards the wall behind you. This is what your shoulders need to be doing in the handstand; they need to be pushing open, not simply relaxing.
Once you've developed a feel for this, THEN it will be much easier to address problem #2: the arch itself. Remember that the hollow should not be in the lower back, it should be in the chest and upper back. I find the easiest way to think about it is to think about keeping your back round. And remember, it should be a very very slightly hollow -- just enough that you know you aren't arching. Handstands with your belly against a wall can sometimes help this -- the goal being to get your hands as close to the wall as possible without falling. This forces a straight body, since any bend will pull your weight away from the wall.
Ill also work on my strength and flexibility. I have terrible flexibility, from my hamstrings, to my hips, to my glutes, etc. But i "passed" the Thomas test, with my legs bent...but not with my leg straight (i can barely get my legs past 90 degrees straight-flexibility is that bad )