for the ship bingo, Barry/Hartley and Barry/Cisco/Hartley? :)
Barry/Hartley - PiperFlash
I love this ship. It's an underrated ship to me, could do with more attention. I don't know that I'd call it cute specifically, though it can be.
They've got the enemies to lovers angle that I enjoy so much. I would, and do, read fics about them. And I write fics about them too.
There are a lot of parallels between Barry and Hartley, most especially in how Eobard treats them both as his special 'chosen' ones. And he lifted them both up with the intention of throwing them away. So I really like the idea of the two of them healing together. Though Eobard isn't all they have in common and it's interesting to examine those too.
Hartley's estranged from his family and it's not hard to imagine that Barry's belief in his father not only caused friction with Joe but with any bio-family he might have left. Shared interests in science - Hartley's a physicist and physics is a big part of the track taken to become a CSI. They're both scifi and fantasy nerds...
There's just a lot going on there that makes them an interesting ship.
Barry/Cisco/Hartley - PiperFlashVibe
Okay so this one I do find to be a cute ot3 but that's because the Cisco/Barry side is already adorable in their canon friendship. Those two are just adorable together and I have no doubt that adding in Hartley would just make their cuteness more dangerous.
My points about Barry/Hartley carry over to Barry/Cisco/Hartley. All three of them have a lot of things in common to draw them together. And if they spent the time and effort on building a relationship, then I could see them being very happy together. With a bed big enough for all three to cuddle. :D