I went on my boyfriend's facebook and saw him and his ex flirting with each other?

she was telling him she misses him he was telling her he missed her more and she called her mother his ex mother in law and hes like ex? your still my wife i dont care :( and she was calling him babe and she was like i love you to him and he said he loves her too and she was like it upsets her that she can't be with him and he was like you go out with another boy and thats why you cant have me. i really don't know what to do. i know i shouldn't have been in his facebook but i was thinking ALL DAY and i just wondered if he spoke to any other girls like that and it turns out he was with his ex that he dated for a year. and i mean we been going out for a little under a month and i really like him but why would he be talking to his ex in this way :( and i think they probably text each other too because in the beginning of the conversation he said why didnt you just text me. im so upset please help i need advice! what do i do! dont know if i should let him know i saw the conversation cause then i look untrustworthy =\ but he was the one talking to his ex !