If Dad is providing credit you don't have, chances are his tax bracket is going to be a lot higher than yours. Having him pay the taxes on the profit may not be a good idea. The cleanest method would be to have him pay you "your" profit via a 1099 for services provided- in other words, just as you suggested he writes you a check then sends you the tax form. Then you pay income/self employment taxes on this, assuming it is a flip.
For the future- form an LLC; just file the form, no operating agreement necesary between just you and your obviously helpful dad. Run all your purchases, sales, etc. through the LLC, with Dad personally backing the loans. Distribute the profit as per your agreement, and it will be treated as though the LLC doesn't exist as it is a "pass through" entity. Ideally, rent the property for the one year holding period so you pay Capital Gains instead of income and SE tax, save yourself a bundle. (You can still do this with your current property, and with the lender's approval ["my financial advisor insists..."] still put it in an LLC also.)
Chris