I want to put up my capital for the rehab of one possibly two homes. I wouldn't be doing any of the actual work but just providing the flipper with the funds. As an investor, how are my returns structured? What's typical? I.e 50/50 of the profit or a % of the profit?

You can structure it however you want.  One way is you get 100% of your investment back first.  Then you get 1% of that amount for each month (12%/year) and then split it 50/50 on the profits.  If the guy is good, then he would agree

There are a couple ways to structure this but the first thing you'll want to figure out is if you and the flipper are partners or if you're just the lender on the deal.  If you're partners, you could split the profits however you want (50/50 or whatever you two agree is fair).  But you would also split any losses if the deal doesn't make money.

On the other hand, if you're just the lender, you get paid a fixed percentage/return on the money you loan to the flipper while they do all the work.  You're due this money whether or not they make money on the flip, and any profits/losses from the flip are solely theirs.

A little bit oversimplified, but that's basically a couple different ways you could structure this. 

If all you're doing is lending money, if I were the other party, I'd prefer to just treat you as a lender and pay interest on the loan.