So just want to know if she has any excuses of mana transferring to do that
Guessed as much xP
Well about Kuro / Chloe, in the manga she's also really affectionate when transfering mana with any girl, but something could happen between them, the reason she's like that is probably because if they have to kiss they can at least enjoy it, and fanservice obviously, I don't know how they made in the anime but in the manga as the story advances it's obvious that they could end as a couple but will probably stay as sisters, in this version Kiritsugu and Irisviel didn't die and ended the 4th war, because of that Stay Night never happened and Illya can live as a normal child, she never had any training in magic so she can't transfer mana in other ways, doubt Rin and Luviagelita would want to lose time teaching other ways as Illya don't know anything and she can just give a kiss.
Miyu is the one that is really gay for Illya, if a pairing would happen it would be Illya x Miyu, as the story advances they don't leave doubt that, besides Miyu brother, Illya is the most important person for her and that she's pretty much in love with Illya who don't really do much to discourage Miyu.
The serie starts as a parody, so the first manga and it's sequel 2wei it was unlikely to have any real yuri as it's a lighthearted serie most of the time and used yuri in part for fanservice and comedy, but 3rei starts to get a lot more serious like main series of Type-moon so now we have small chance of having something serious between them, the problem is that exactly because that even if their relationship gets more serious there's good chance of the serie having a bittersweet ending, Miyu is basically Illya of a paralel universe, aparently same world of Fate/Extra so if possible play it before reading 3rei, if the serie continues getting more serious I suspect Kuro will die and Miyu will have to stay in her original world and probably never see each other again, of course it is unlikely but also posible to have a Illya x Miyu x Kuro ending, Type-moon made a threesome ending in Stay Night so technically not impossible to have one in Kaleid Liner if the story don't become too serious and continue to have lighthearted side.