As far as I know, when you use Monero, addresses and amount of coins used in transaction don't appear on blockchain, your IP doesn't appear in network and your anonymity is at its highest level.
Correct, but there are nonetheless small details which can indicate there's a high chance certain coins share the same owner. Let me give you a simple example: You sell 1 BTC for 200 XMR at a no-KYC centralized exchange. Within an hour, you sell the 200 XMR for 1 BTC in another no-KYC centralized exchange. There is clearly no blockchain connection between your bitcoin, but there's a strong implication of two users buying / selling 200 XMR around at the same time, so the two bitcoins may be linked given the CEX operators share that kind of information with third parties.
In decentralized exchanges that's less likely to occur, but it's possible. Time is a parameter which can enhance or ruin someone's privacy, dependently on how you use it.
Logically, when you use Monero's full anonymity, no exchange should be able to judge you.
That didn't age well. No regulated exchange accepts Monero as far as I know, because everyone who wants to be anonymous is guilty.
Is there any flaw where BA companies can catch you when you use Monero stealth address?
None that I'm aware of. The US government has issued bounty for anyone breaking Monero which is yet unclaimed.
