I think it's about 4 months that the beak reaches its worst and stays there. It will keep growing and may need periodic trims, but the angle of the cross beak stabilizes around there, and certainly by maturity.
As your chicken's beak gets worse, just make sure he actually is eating enough. My cross beak used to be a very flighty bird that didn't want to be touched so I didn't realize how skinny she was getting as her cross beak progressed. I fed her separately from the other chickens twice a day using a giant bowl and she pecked at it nonstop and it looked like she was eating. Then one day at 3-4 months old, she flew in my arms squawking (desperately hungry) and she was nothing but skin and bones. After she ate from the bowl for over an hour, I checked her crop and it felt empty. All those times I'd been feeding her, she was hardly picking up anything and slowly starving to death.
What she really needed was mash (wettened crumbles about the consistency of oatmeal) but it took a lot of work on my part to convince her to eat it. I cried the day she finally ate it. I was getting close to killing her because she was slowly starving to death and only wanted to eat the dry crumbles she couldn't pick up (I tried even giving her scrambled egg, oatmeal, yogurt, scratch, etc. - she wanted none of it). Now that she does eat mash, she is healthy and happy. I check her crop after every meal to make sure it's full. I feed it to her 2-3 times a day, separate from the flock. So as your boy grows, please check his crop and make sure he's not getting skinny.
Another thing to keep in mind is that cross beaks sometimes have trouble with preening. Some say they are at an increased risk for external parasites because of this, but I haven't had a problem. I have noticed that my cross beak doesn't do as well on the really cold nights and I think this is because she isn't preening her feathers as well and so they aren't insulating her as well. On extremely cold nights, I bring her inside.
Cross beaks are extra work and time if their beaks are really crooked, but if you are able to do it, the relationship you build with them is really special. Cheesy, I know, but I have a closeness with mine that I never could have had if she were a normal bird.