"I'm flattered" almost always has a positive connotation to it. It means "It's nice of you to say". It's usually said when someone complements you. For example, A: You look so beautiful today. B: Thank you. I'm flattered. Just like the adjective "flattering" means it's complimentary or favorable. For example "I really love this coat. It's flattering".

It totally depends on the context and the tone. For me, flattery is generally positive, but flattery can also be sarcastic or inauthentic, in which case it is negative.

To “flatter” someone usually means the praise they are giving is insincere. So, yes, that has a negative connotation. But if someone says “I’m flattered” by something, it has a more positive connotation, meaning “I’m honored” or “I’m pleased.”

Why do you think it has a negative connotation? If someone says they are flattered it just means they accept the compliment you gave etc. For example: you’re are such a great writer, I’m sure you’ll make a great author one day. Response: thank you, I’m flattered.