He does have a rather flat jump, but he's also standing off a good bit from the fence. Standing off, IMO, is better than a natural chipper. Once he's developed more, I would think your trainer would start asking for a more rounded energetic canter. Right now, it's just forward. That will help him get the ideal distance and have a rounder jump. Also grids will tighten up his form, teach him to round his back and use himself more effectively.
I am personally against any equipment such as martingales, especially for young horses. You're horse truly isn't rounded and on the bit if you must use a tool that restricts their head. I suspect you won't need it once he's carrying himself properly and is on the bit, but that is flat work.
For not having a lot of experience jumping, he seems very willing and happy about the work. He will probably be easy to polish into a show horse.