I think it might be the brotherhood part of it that Kon doesn't quite get... How wonderful it is to Tim to have a family that loves him, *knows* him. I think this Dick knows Tim had a bit of a crush, early on, but genuinely thinks that Tim got over it, instead of just better at hiding.

Whether Dick is bisexual or not, I really feel like it would be a fundamentally bad idea for he and Tim to attempt a hook-up. As much as I believe they adore each other, in their own ways, there's just an imbalance there. It's something I've tried to address before... Tim revolves around Dick the way Dick revolves around Bruce... But Tim's not the only one in Dick's orbit. He's been orbiting the longest, and the most obsessively (unless you count Bruce and Dick as binary stars, which might not be far off), but he's sort of been circling at a distance for so long...