Any time I hear someone telling me, or anyone else, how honest they are, a line from Hamlet comes to mind:
"The lady doth protest too much, methinks."

I'd say, "Great! I think most people ARE honest, don't you?" And get into a long, deep discussion about honesty.

It sets off alarms for me. I ask myself, 'why would a total stranger feel the need to convince me of their integrity?' Only if they plan to lie. The phrase, "You can trust me." has the same effect.

For starters...I have never thought a person needs to profess his honesty...we need evidence for truth, at least I know I do!

Need more info:
What is the context?
What is the interaction?
Honest about what?

I trust them about as far as I can throw them.

I always assume someone is honest until they prove me wrong. When someone tells me they are honest l am suspicious. Why would you assume l would think you are not.

Honesty is something that needs to be demonstrated over time. Not simply asserted.

That's a huge red flag! I have had the same experience, in business, when people found it important to announce, shortly after we met, "I are a Christian". Then when something new comes up the they "have to pray on it". That only happened a few times and each time the "Christian" pretty blatantly attempted to rip me off or proved themselves to be degenerates.

I say, "OK" then I either go about my business like normal, continue whatever conversation we are having, or let them explain why they are honest then I change the subject to something more interesting.

True honesty is demonstrated, not told.

That person is the Judge, jury and the accused...

Sounds fishy to me. Next they’ll be asking for money.

Best be careful.

"Believe me, many people say I'm honest...very stable and honest!"

I tell them that eventually I will know rather or not that is true.

Honest and intelligent people have no reason to state such things about themselves.

I would evaluate their need to tell you such. Why do they feel it important to convince you of that? But yea, Red Flag, honestly

They are dishonest. Claiming of honesty is dishonesty. (আপনারে ভালো বলে ভালো সেই নয় ৷ লোকে যারে ভালো বলে ভালো সেই হয় ৷) (AAPONARAE BHAALO BOLAE BHAALO SEI NOY . LOKAE JAARAE BHAALO BAOLE BHAALO SEI HOY)This is a bengali proverb which means if says he is honest , then heor she is not honest . Whom the people says honest then he or she would be the honest.

It depends what they say in that one sentence.

he's gaslighting or soon will be

Never ....that's a red flag right off the bat. RUN!

Agreed, anyone you don't know that has to "prefix" a statement to manipulate you into their frame of reference.... worst yet are those that use gaslighting tactics to put you on the defensive or invoke a emotional response to a clearly deceptive premise.

One should stand by what they say and more importantly what they due.

Kuato:
You are what you do. A man is defined by his actions, not his memory.

I will ask: what do you mean being honest? Maybe this person will answer but keep asking questions until this person gets tired. "Scammers"

Do not believe them! Truly honest people never give it a thought...have You ever said that to anybody?

Sure now! And I'm the Pope in Rome!