6 years and 1 month - rated 1140 in classical chess online

My son is 6 years and 1 month - rated 1140 in classical chess online on another site after 100 or so games and he's played thousands of the 5 minute games.  Where is his skill level based on his age?  What are some paths for him to compete with his age group? 

Sign him up for a local USCF-rated tournament. Many places have "scholastic" USCF-rated tournaments, which are just for kids.

He hasn't played a ton of other kids actually except online.  He thinks 3-4 steps ahead consistently and can beat me sometimes and I'm around a 1200.  We moved to Italy.  I think I found a chess club here in Naples he can get some live experience.  He understands end games well.  I'm going to teach him the opening book next.  He seems ready.  He's also doing 5 grade math, knows fractions and multiplication before he turned 5, etc.  I want to push him some, but not too hard.  I'd rather have him playing and studying chess than playing video games.  

There's not much link between chess and math. Just because he's good a math doesn't mean he'll be good a chess... just food for thought.

The best way to improve in anything is to compete, and chess works the same.  So having him in the club is a great first step. Next will be to ask the club for some local chess tournament details.

Also, don't set him up for failure. Make the competition outcome always good by giving a reward for losing as well as for winning.

God, I wish I had something comparable like Lichess or Chess.com at my avail when I was his age ... If he perseveres, he'll be doing great. Kids adapt new knowledge very quickly.

"... for those that want to be as good as they can be, they'll have to work hard.
Play opponents who are better than you … . Learn basic endgames. Create a simple opening repertoire (understanding the moves are far more important than memorizing them). Study tactics. And pick up tons of patterns. That’s the drumbeat of success. ..." - IM Jeremy Silman (December 27, 2018)
https://www.chess.com/article/view/little-things-that-help-your-game

Thanks for the advice.  I came here not really knowing what to show him and asking for advice, not to be ridiculed.  I could have posted a ton of other things about the family if I wanted to boast about intelligence, I just wanted to give a baseline for some sort of group analysis that I thought might help give a baseline.  

I am curious, why is teaching openings bad?  He's waaaay beyond beginner.  I used the opening app in parallel to my games and I've been able to not only memorize the openings, but figure out opening theory along the way.  Clearing out center pawns, destroying castles, doubling pawn etc.  It seems super simple to play with an app to help get that under your belt. 

He has studied the endgames and all the chess kids videos. 

I will surely look at the other study methods mentioned above.  

Thanks for the input!  

Is there an online chess club for 6 year old kids that is private other than chess'kids'?  I'd like to let him play the best at his age group if there is a way online.   

Not everyone thinks so. I think that there is general agreement that one can spend too much time on opening study.

"... for those that want to be as good as they can be, they'll have to work hard.
Play opponents who are better than you … . Learn basic endgames. Create a simple opening repertoire (understanding the moves are far more important than memorizing them). Study tactics. And pick up tons of patterns. That’s the drumbeat of success. ..." - IM Jeremy Silman (December 27, 2018)
https://www.chess.com/article/view/little-things-that-help-your-game

Yeah, how much does a pattern weigh, anyway? Of course, the quote is from an entire article on "little things that help your game". (I produced the quote because of the reference to opening study.)

How well a person plays chess says nothing about who they are as a human being.

Are those the only two options? Books like First Steps: 1 e4 e5 and First Steps: Queen's Gambit
https://www.newinchess.com/media/wysiwyg/product_pdf/7790.pdf

https://chesscafe.com/book-reviews/first-steps-1-e4-e5-by-john-emms/
https://www.newinchess.com/media/wysiwyg/product_pdf/7652.pdf
are potential sources of games with explanations intended for those just starting to learn about an opening.

What's classical chess online?!

Is markmax33 the parent? ("... I came here not really knowing what to show him ...") Do you have a comment about the EnergizeMrSpock suggestion to have the "kid play through wins by Morphy, Tarrasch, Capablanca, Keres and later, Bronstein"? Is there a reason why the parent should not consider showing the child a game from the sort of book that I mentioned?

he has caught the chess bug at the best age (your son) his mind is a sponge for knowledge and can absorb a lot more than youd think , but youre right to not want to push him , as this may deter him , from the game for a bit , most juniors with encouragement are very good at chess , and most seniors have a tale to tell of when they faced a junior who took them to the cleaners

yes to the naples chess club , he will find good challenges to his ability , this is healthy for any chess player

Books like First Steps: 1 e4 e5 and First Steps: Queen's Gambit are potential sources of games with explanations intended for those just starting to learn about an opening.

As I said - those books are for adults and not kids. The other suggestions are equally ridiculous, but those guys don't post reams of the same thing in response to every question on this forum.