FHA is only 3.5% down plus closing costs.

Your parents are allowed to gift you funds to purchase the property.

There is a way to gift equity, but you will need to speak directly to your lender about the acceptable way to have that gift of equity on this purchase.

Yes, it is a stumbling block that your parents own the house now. There are additional lending guidelines for this type of sale. This is in no way an arms length transaction and that is part of the difficulty with financing.

The difficult part in this transaction, that I see, is that your parents just purchased the home less than a year ago (in addition to the fact that you are buying a flip from your parents) so the lender may have to use a lower valuation than the new value. Possibly even their purchase price last December. It is likely you will need to have two appraisals on this property to meet guidelines. However, having said that, the guidelines are loosening up from where they were a few years ago so if you are going to pursue this purchase, this is a good time to do it.

You will need to discuss this with a very knowledgeable loan officer. Stay away from big box banks and go straight to a non-bank lender like Guaranteed Rate. I say that because you need someone that can underwrite, fund and close an FHA loan directly and has a knowledgeable experienced loan officer to help you negotiate this financing. I have an excellent LO if you need someone just pm me (no obligation). This will be critical to you in this purchase.