It's an automatic warning when your rating crosses a high threshold. They don't think you're cheating. You can ignore it.
Flagged for suspicious play

That's something I haven't heard of. I'd say contact the support team. https://support.chess.com/customer/portal/emails/new

Thank you for the help.
They say they will try to reply in 1-2 business days which in my mind is ridiculous, as the problem is of their own making.

It's an automatic warning when your rating crosses a high threshold. They don't think you're cheating. You can ignore it.
His rating is not much higher than my highest rating and I never received any kind of warning...

Maybe things have changed. From what I remember, after you peak at a certain rating, they send you a message about how they're on the lookout for cheating.

Interesting that two of the people posting on this thread already closed their accounts. I'm sure it is just a coincidence.

Basically, it amounts to this: if you make moves that happen to coincide with some cheat engine, they just ASSUME you are using one... which is BS. And from what I understand, not only is this monitored arbitrarily, it is automated. They don't even have to actually catch you to cheating to accuse you, and reprimand you, for it!
There are only so many ways to sensibly play the Fried Liver, Owen, Center Game, Wayward Queen, etc. nonsense that sooooo many of the weaker players on this site use almost habitually! They play it nearly every single game! You would be a fool not to play the same moves that Stockfish or whatever happens to suggest. I guess I am expected not to make a reasonable move, because... Oh! Some unknown moderator might think I'm cheating! It would seem that "potentially suspicious" is a synonym for "sound chess strategy."
Chess.com should have to actually catch you in the act in order to punish you for cheating. Which is to say nothing of the people who just stop playing when they lose and let time run out, which is a much more serious problem here than some wise guy trying to use an engine.
I think you are wrong about it being automated. They don't reveal a lot of info but they have said that real people make the final decisions. And nobody is going to be banned for knowing the first ten or fifteen or even twenty moves of some lines, because we all vary at some point, in sad but human ways from the computer's top choices.
I came back to this site and started to play standard games. I won all of them, but this is to be expected since my strength is higher than 1800. In fact I was not paying attention in many of the games. I have just gotten a message that I am flagged for cheating which is maybe reasonable. But my game seeks are delayed, and so it is impossible to find a game. When can I expect chess.com to look into this?