This from the anime so it's probably FILLER but Kagura was interested in Hirashi Hongo in episode 189.
He's the sick kid who does the radio exercises with Kagura, she blushes at some parts of the episode when she's talking with him.
I wasn't sure whether he died or not at the end of the episode though.
As for who should pair up with Kagura, Okita seems most likely to me at the moment, he probably at most 10 years older then Kagura ( I don't know everyone's age)
GIn would be too old, although I can see her father Ume Bouzu accpeting Gin into the family and age doesn't really matter in love I guess.
AS for Shinpachi, they seem like they have a sibling or nakama relationship then anything else, I don;t think Shinpachi would ever see Kagura romantically or vice versa.
My money would be on a a totally new character.