I definitely think there was something deep between Fai and Ashura, whether or not that something was romantic love could be debated, but I think it's a clear possibility. Their relationship has a lot of room for speculation right now, as far as I see it.
One, we know that Fai is running away from Ashura, but while this implies that he fears him (as is further proven by his reaction to his name in Sharano) it does not necessarily mean hatred or even, really, that Ashura did something bad. In fact, Fai wishes Ashura sweet dreams before he leaves, which is definitely an affectionate gesture.
I haven't read much of RG Veda, but as it's been said, Ashura really didn't seem to care for much besides his son. So thje fact that Fai seems to think Ashura will chase him is perhaps significant. Why would he?
The two most popular theories seem to be that he needs him for some reason, or he *wants* him for some reason. I don't think he's intending to kill him, but I don't think whatever he has in store for Fai will be easy to deal with since Fai is running away.
There's still the matter of all the dead bodies, which could imply that Fai and Ashura had a violent confrontation, or it could mean nothing. The fact that Fai wishes to never see Ashura again and wants to get away to a place "without" Ashura is an odd reaction to have to someone, I think. Not hostility, not a desire to defeat or get rid of Ashura or harm him in any way, just to get away from him. Personally, while it doesn't mean that one of them betrayed the other, Fai's reaction to him reminds me of someone who was betrayed.
I don't like to think of Ashura betraying Fai, or Fai betraying Ashura, but Fai is acting how I acted when I was betrayed by someone close to me. I didn't want them hurt, I just wanted to get *away* from them and never look at them again. Though, really, just because *I* felt that way doesn't mean it's the same with Fai since he's, well, a manga character and everyone reacts in different ways.
Anyway. Personally I think Kurogane/Fai is going to be the Fai-pairing in the end, especially the way their relationship is being developed in recent chapters, but as everyone's been saying, it's just an opinion. I still think that there's a large possibility of Ashura/Fai becoming canon, but I don't consider it canon juuust yet. Though I am a believer that they did have a deep, non-violent relationship.
As for KuroTomo, I agree with Becster. I personally don't see *any* romantic chemistry between them at all, but I do agree they love each other. I just don't think that they care for each other in a romantic way. Though, yes, that's just my opinion as well.