R66, it's unclear. I had always thought just friends - close but completely platonic. However, in October 2019 there was a post on another thread which claimed a friend of the poster had seen them making out in the audience at a performance of a play in New York. Quotes from that post and the next couple of comments afterwards:

"Moving back to actual gossip about the cast, a friend got tickets to see Slave Play on Broadway a couple of weeks ago and was sitting near Gwendoline Christie and Finn Jones, who were making out during the performance. Not gonna lie, I was kinda shocked. I was convinced he was in the glass closet. Maybe he’s bi? Also, WTF is the deal with Gwendoline’s relationship? Is she bearding, or is it just wide open? "

reply 240 10/30/2019

"[R240] do people really make out at Broadway shows? that's tacky"

reply 241 10/30/2019

"[R241] I guess that’s why my friend mentioned it. Nobody gives a crap about seeing actors in New York, but seeing two people from GoT all over each other during a play was noteworthy. "

reply 242 10/30/2019

I don't know how to link directly to the post, but if you click on the link to the thread below, and scroll down to reply 240, you can read the original comments from there on.

I do remember being online at the time when he was attending that show with Gwen, and he did actually post a few things which he quickly deleted. The first was a clear shot of both their faces, which he deleted shortly afterwards and replaced with a shot of just the upper half of their faces. Then there was a shot praising the play they were seeing. He ended up deleting both of those as well, and several hours before the usual 24 hours that stories can last for.

On the one hand, if they were friends-with-benefits, would they take the risk of being seen kissing in public when Gwen was and is dating someone else (Giles Deacon)? There has always been speculation that she and Deacon have an open relationship, but as neither have said this publicly (obviously), I would imagine they would be discreet about any side relationships they might have, whereas kissing your FWB in the middle of a theatre audience is the opposite of that approach. On the other hand, I can't see any reason for someone to just make up a story about seeing them making out, and Finn deleting early all the things showing they had been out together that evening is curious. That said, this is the first and only time I've heard gossip about Finn and Gwen being more than friends, and they've known each other for more than ten years now. So I'm not sure what to make of it all.