Me [26F] with my SO [29M] of 1yr. I don't like him contacting his ex. Am I being overly jealous?

Throwaway account. I don't like my SO messaging his ex (Kate), that's basically the crux of it at this point.

My SO is an incredibly bold individual, open, romantic and we have an amazing relationship. We've been together for a year and we've known each other for two years. We are pretty good when it comes to communication, we are open with problems and discuss them til we get to a solution, this usually happens quickly because he hates drama and I don't want to stew over negative emotional crap. Please note that the openness is why there's so much information below. Ie: how do I know there's compromising pictures of her on his phone? Because I've seen them when he's scrolled past them looking for a picture to show me. Like I said, he's open and if I have a problem with anything, he expects me to be upfront with him about it and he's the same with me.

My SO is friends with Kate, they were an item about 10 years ago and lost contact when the relationship ended. About four years ago he got back in to contact with Kate (this is before I met him). They've met up a few times prior to me being in the picture and became firm friends and his best friend thinks she's fantastic. During one of these meet ups, he said he loved her and he's sent her chocolates for Valentine's Day and incredibly thoughtful gifts, although sporadically.

Before he and I were dating exclusively, we both went on dates with others and he flirted with Kate, they weren't in the same city so it was mostly via messaging (pictures were sent etc, including nsfw ones). He still has these pictures. I'm fine that he flirted with her during this period because we had defined our relationship that way, it's after we became exclusive that I feel that he hasn't respected the boundaries of an exclusive relationship.

He thinks she's gorgeous, she's his type physically, more so than I am and he still flirts with her and jokingly asks her to marry him. She seems like an amazing woman and she's currently dating a guy and I'm assuming her to be a standup woman who brushes my SO off when he flirts with her because she's known him for so long.

Whenever he gets texts at night, it's from her and I hear him laugh and get a stab of jealousy. I also think it is incredibly rude because it's usually a Friday or Saturday night and we are out at dinner or with friends and it takes him away from the event. This isn't just regular jealousy, I know he loves women and they love him and I'm fine with it, sure I may get a little jealous but there's nothing nasty going on because I know he loves socialising and I won't prevent him from that. It's just this one woman and I don't know why I'm having such a hard time with it. I know that I am misplacing my anger and starting to hate this woman that I have never even met (although I will be meeting her before the year is over).

I've only brought this up with him once and it did not go well. I got mad and even though I was trying to explain to him my issue with this, he became very angry and so I backed off. He said that they sent each other pictures to keep track of each other, stay in each other's lives like normal friends do. Problem is, these are nsfw pics and they're 2-3 years old, why does he still have them? He's not with her and he won't be with her because she's in a serious long term relationship with another guy. I don't like fights to drag out so I expressed that to him but he ended up sleeping separate from me that night. The issue wasn't addressed the following morning.

We also did nothing for my birthday that we had planned prior because the weather ruined things, and I was understanding about that, but I barely got a happy birthday. Kate's birthday is around the same time as mine and she got a thoughtful message from him that he posted on fb and it hurt a little bit. She gets a thoughtful message and I get nothing because of the weather? I mean, you can write me a note on a sheet of paper ripped from a notebook.. I'll end this here because I'm all over the place. We otherwise have an amazing relationship, we talk, laugh, sex life is fantastic, we have no major issues in our relationship at all. His parents love me and mine love him.

Basically, am I crazy? Am I allowed to not like that he flirts with her and still has nsfw pics of her on his phone? Am I allowed to be upset over this? Do I bring it up to my SO again? My SO has known her for a long time and she'll always be around, so how do I deal with this?

Tl;dr: boyfriend of 1yr has nsfw pics of his ex (which he hasn't even tried to hide) who is still a very good friend of his and he flirts with her over messaging apps. He also removes himself from social situations for ~15min periods to chat with her which I find to be rude. How do I deal with this? Both with him and just by myself (ie: am I being overly jealous?)

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