Amazing camps for kids who only want to coach?

Trying to put this a bit gently:  paying dues IS "the real work". A huge part of it. So establishing that a 10 year old will only benefit from work with high performing programs and working with really talented coaches probably is not the best starting point.

As far as your son's limitations, when you describe his physical nature, and then say "profoundly gifted in math", as an educator it sounds like he may fall on "the spectrum" as it is called now. When you say he has no hope of playing football, do you mean VArsity and above? Because he absolutely could play youth- ESPECIALLY now that flag football is surging in popularity.

If the spectrum aspect is accurate then one of  his biggest challenges to COACHING is that coaching is all about relationships. I would argue that playing football will help develop relationship building skills more than trying to start a coaching career at the age of 10.  It will also help him appreciate the actual skills required.  

In the coaching profession, it is quite commonly stated that coaching the position you played is a net negative. Coaching a new position forces one to really improve as a coach in many facets of the profession.  HOWEVER-- I will say that I do find one aspect of this practice to be challenging-- understanding what you are asking the players to do and the difficulties they incur while doing it.  It is one thing to bark at your ILB that they need to key the near back through the guard, not false stepping, and making the appropriate decision and reaction based on that read while being able to shed downblocks from OTs/TEs etc.   It is another to actually experience all the sensory input  all that is required to be instantly processed. 

Your boy playing ball might help with that.  

EDITED IN-  Also, keep in mind that player development is far more important to almost every coaching situation than the schemes or "strategies"  All of the iceberg memes on the internet highlighting how much bigger the part you don't see is absolutely applies to coaching. People see a play on tv not work and just assume that the coach chose the wrong # off of his giant double sided color coded laminated play sheet. That is a minute aspect of the job. 

Now as he progresses into the future, his aptitude with math could be leveraged with coding/data science etc. to work into an analyst role. That seems to be the rage now...if it still holds weight in the future that could be his in.

It may be enough learning for him now.  Coaching with a club of players about his age could be exactly the experience he needs to start off with.  He may find it more sophisticated than he thinks, just because it's not the pros.  It would probably be hard for him to coach formally, as the clubs have age requirements for insurance reasons, but there are many opportunities to sneak helpers onto the field informally, especially since to all appearances he could just be one of the players -- and that's if he doesn't want to play or is medically unsuitable.

As to the suggestion of analytics, that could be a very good idea at the right time.  Handicappers can make a lot of money, and so can the people who do research for them.

Have him volunteer to be a manager for his high school
Or junior high teams. He will learn a lot just being around coaches and being able to ask questions

At 10 years old I was going to play for St Louis Cardinals. It would be another 4 years before I had any interest in coaching or playing football. I'd never even watched a football game on TV until the 85 Bears.

Point being, he's 10. Let him explore, but let's not also forget he may want to do something entirely different when he's 10 1/2.