How do I reroll? Just delete the game? Can I sync my data between my iPad and iPhone?
There are a few ways to reroll.
Easiest
While this is indeed the easiest way, it's also the most time consuming. You basically delete and reinstall the app after the tutorial if you don't get the roll you want. It has to download all of the updates every time, but it does the job.
Harder
I have not tried this, but I imagine it works the way I'm thinking. After you get to the tutorial, you can backup the data files that pertain to the updates. So everything except the file the represents your main data. I don't know which file this is, so someone else would need to help you here.
But the basic idea is that you only have to go through the trouble of updating the files one time. I think there's a guide on the PAD group page, but I haven't really checked. It's worth hunting around to see if it's possible without updating, though.
With regards to playing on multiple devices, technically you could, yes. You need to make a copy of your data and transfer it to your other iDevice. But I would be wary of this - there COULD be some sync issues. I mean, I know it's all server based, but there's a chance. I don't know if it's against the TOS, either. My suggestion would be to play on one device as exclusively as you can and only transfer data when you need to.
Again, I've never dealt with this (I have my iPad account somewhere, but I don't play it anymore). I couldn't give you ALL of the tips and tricks, but I can say that when I was rerolling my account "back in the day" for an Amaterasu (since she was the one to get when the game first came out, ha), I just deleted and reinstalled.
Good luck!
Haven't played in a while, so after about 5 entry rerolls I got an AA Luci.
I'm wondering though if I should just go at it until I get a Kirin, which I kinda want as a starter.
Luci and Kirin are both exceptional monsters. The benefit of each is that neither
require any IAP to be successful. You can't go wrong with either. If you're just starting back, definitely backup Luci (or donate the backup to someone who wants him instead of Kirin) and start rerolling.