Cheating flag but not banned? How to prove not cheating?

I am apparently flagged for cheating and no longer allowed to play rated games, however my account is still open and I can play unrated games. I'm curious why this can happen. What kind of proof can be provided to lichess to show that one hasn't been cheating?

You can appeal. To be honest, I don't see it, looking at your game history. There are blunders and mistakes on both sides and to me at least it simply looks like your opponents made the last mistake. And your average centipawn loss looks typical, too. In the 50-80s on average against similarly rated opponents; like teens to 40s against lower rated ones.

I didn't look at EVERY game, but I see nothing at all suspicious in the dozen or so I did look at. Appeal: lichess.org/page/appeal

It is possible that you got banned for something other than engine use, so keep that in mind too. If you have been outright abusive in chat or something, for example. Or if you use multiple accounts. Cheating isn't the only reason accounts are banned.

Thanks @phoenixshade for the response. I appealed and they said that I used an engine :/. Not sure if I can prove it one way or the other

What you're seeing is normal. Lichess typically doesn't close/ban accused cheaters' accounts, they just mark the account as cheater and forbid the account from playing rated games.
Disclaimer, I am not a moderator.

@MrScribbles yes I like the disclaimer part.
More than 5 guys I met (who were new to forums) thought that patrons were moderators and asked them to remove the cheat mark.
Also there was this one guy who blamed Lichess for "lying" because a patron had said some incorrect facts about Lichess and he had thought the patron was a moderator.

DISCLAIMER: I am not a moderator.