I hate kayle jungle. It's not impossible to do, I just don't like it because I feel I go way too low from early clears to be able to gank and/or will die if I get invaded. Also she is a champion who is incredibly item dependent, who if she has max items will do a TON of damage if built either AP or AD, but actually getting those items is a real hurdle in the jungle, as they are incredibly expensive. She herself is an okay champion, her ult being game changing if you are able to apply it at the right time, but she received a lot of nerfs because she was so strong, so she pales in comparison to how she was before. If you like it, you can try it out. She should only costs 450 ip I think, which isn't too much of a sink for a champion who is pretty decent.
I will reiterate, though, that you should probably wait until you reach 30 before you really want to jungle. As jungle is optimized for level 30's, with a full page of runes and all the masteries, having less then the full page already cripples yourself even further if you're using a lower tier jungler. Outside of Fiddle and WW, I don't really know of many junglers that I'd personally want to run without at least the bare minimum of level 20(this is when you can finally buy tier 3 runes). Oh, Nunu is another jungler that works incredibly well despite not having all the possible runes/masters and I keep feeling there was a 4th one that existed, I just can't remember who it was. I'm thinking it might be Rammus, but not too sure.
Oh and if you can handle it with no having maxed out masteries/runes, go for it. I'm not saying "do not do it". It's just something that I personally can't handle doing because I tried doing it on my smurf before I got it to 30 and I REALLY hated it because I was used to all my free stats from masteries/runes that I took for granted. Good Luck. Oh and if you have more questions, you can ask, just not promising I'll respond immediately.