WoR Spoilers
I think that from what was thought and said during their time in the chasms, they developed some fondness for one another after learning how similar their stories are. However, I feel that Shallan explained pretty well afterward (to herself and the reader) that she would rather be with Adolin. If Adolin were not there to dwarf it, I could see Kaladin being Shallan's main romantic interest.
Now Kaladin, on the other hand, did show fondness for Shallan as well, but from his statements, (eg. that he would never fall in love with a Lighteyed woman,) it is likely that he is not actually in love with her romantically, but feels that they are related by experience. His aversion to Lighteyed girls could be based off his general dislike for Lighteyes or his previous romantic encounters, (Tarah, Laral), Tarah being the Darkeyes he met during his time in Amaram's army and Laral being his childhood friend turned Brightlady.
In my opinion, he does like Shallan, but not romantically, or is at least happy to let her be with Adolin, he mentions at some point after getting out of the chasm that he liked Adolin, and thought they were a good match for one another.
I am not sure of how their opinions of each other have changed since they both got their Suddenly Radiant powers.
I am interested on how this will effect his aversion to Lighteyed Women, as we do not have enough information to determine the reason for it, but I can imagine he will be torn about his new Light Eyes.
Wow, that got a little convoluted. I'll just summarize it.
Kaladin and Shallan like each other but are fine with ShallanxAdolin.
Oh, and I just thought of some ship names, they've probably already been thought up but #Shadolan, #Shalladin, #Dalinavani, #JasnahKhohoid