I think its a forgone conclusion that Jon is Rhaegar and Lyanna's son. People only doubt it because they think it was too easy to put the puzzle together and they know GRRM has a tendency to troll nikkas.
You had Rhaegar, a 23 year old prince obsessed about this stupid prophecy. The Prince that was Promised....
the Song of Ice and Fire. I think he met Lyanna and realized immediately that the prophecy was about the Targaryens and the Starks....the South and the North uniting and he was willing to start a war over it.
Other subtle jabs I notice is the spelling of "Ice and Fire". People don't say "Ice and Fire". They say "Fire and Ice". It sounds better and flows better off the tongue. I think the reason GRRM purposely put it like that is because Jon Snow is a Stark first and foremost (dark hair, dark eyes, raised in the North), and a Targaryen second (not having any of the Targ characteristics).
Another one is the flowers. Lyanna liked wearing a crown of blue petals around her head. That's a pretty odd and unusual thing for a girl to wear, don't you think?
Daenerys had a dream about blue petals. She saw them growing out of a giant wall of ice. Lyanna used to wear Blue Petals
Jon Snow guards a giant wall of ice
Dany also seen a vision of Rhaegar calling out some woman's name as he died. It wasn't Elia