Here's a link you might find helpful:
https://www.chameleonforums.com/prolapse-any-help-would-great-134915/
The general consensus, and it's a good one, is that you should take him to a vet asap. However, the main thing I'll say is that whatever you decide, action should be taken quickly.
If you choose to go to a vet, just realize that some have much more experience with chameleons, and reptiles in general, than do others. Also realize that there are no guarantees. What a vet does, as well as what you may try on your own, may or may not work.
Part way down in the thread I provided a link to, you'll read about an experience that I had. What I did, likely, will only work sometimes. However, if you don't feel comfortable trying, for whatever reason, something like I did, or even know how to firmly secure a chameleon in your hands then definitely go to a vet.
If one of my kids gets sick, my wife and I will always have a judgement call to make as to weather or not to bring them to the doctor. In the same way, I'm not going to say you should definitely go to the vet.
In the end, of course, you'll have to decide for yourself whether you think you can get the intestinal prolapse back inside, something any vet should be able to do, with or without surgery. Also, for anyone that might possibly try putting a prolapsed intestine back inside, it should go without saying that you should first be able to identify exact what it is that is protruding out of the cloaca.
It's very important to note that I had the benefit of watching my vet put a prolapse back inside. I wouldn't have attempted it had I not seen it done. It was much easier than I thought it would be though. Bottom line, if you've never seen it done before, then I would definitely agree with the others here that you should get your chameleon to a vet as soon as possible. Even though there have been reports of prolapses resolving on their own in mild cases, going back inside, if you don't want to take any chances, personally, I wouldn't risk not taking any action. In the prolapses I've experienced with a few of my chameleons, none of them went back in on their own, but they were protruding quite a bit more that what I'm seeing in your pics.
Finally, I'll only add that I would try to find a vet that has experience with chameleons. What my one positive outcome with an intestinal prolapse in one of my chameleons has taught me was simply that stitches are not always necessary. That is as long as you are prepared to get the intestine back inside, without delay, should the prolapse reoccur, which they often do. I may need correction on my view and I'm prepared to take criticism. I'm not a vet after-all, although I do have a friend who is one.
Perry