Both could work but if I am honest, I don't like either sentence because the style makes the exact relationship between the two ideas unclear. I might say more simply: "He felt insulted and that he had been taken advantage of." Is there other context, or can you explain what you want to say in more simple terms? Then it might be possible to reformulate your ideas using these structures.

Technically, both are correct. It's more about style. In sentence one we have an adverbial past-participle phrase that gives more information: the 'reason' for the condition in the main clause. He felt insulted. Why? (He was) taken advantage of. In the second, 'Being' is also an adverbial participle phrase. It too gives a 'reason' for the condition. Being taken advantage of, he felt insulted. = He felt insulted (because he was) being taken advantage of. The only caution I would give is that with the second (although not incorrect) there is a 'shift' in tense that can be confusing. The first sentence is more common for that reason.