And addressing my item #1 comment, almost always, when a "distressed" homeowner is approached, they initially are grateful to have the loan brought current, but before long they forget the circumstances they were in and you become the bad guy that stole their house.

If you Bank/Lender does not allow it you can refinace the mortgage into a DSCR or true Portfolio loan program. 

You can allocate those proceeds any way you want - as equal down payments or buy one for cash and others with loans - It doesn't matter a bit as long as you use all of the cash and purchase at least as much as you sell. 

Here's a breakdown on loan options to consider:FHA Loan: @Brittany Minocchi is right in looking at FHA option.  

@Steve Powers is correct that these were mostly originated as owner occupied loans.

Hey Makani, you should check out DSCR loans, which are primarily for investment properties and focus on the property’s income potential rather than your personal income.

I know that interest on the acquisition loan can be included in the cost basis since it’s inventory.

I flip with cash, not loans, mainly because there are not enough deals out there that meet my highly selective acquisition criteria, so no need to pay interest on cash otherwise sitting in a money market account. 

If it is with HUD, did they foreclose or is HUD servicing the loan? 

Please, no solicitations.Use the renovation/acquisition loan products that require 10% down on the purchase and you should be able to get a few going at a time.