I am a civilian contractor stationed in the Middle East and have no primary residence in the States. 

It'll be non-traditional financing though.

As long as they sell it when they can still claim to have lived in it for 2 out of the 5 years prior to sale then they will get the $500K primary residence exemption. 

Currently, I am traveling and I do not have a primary residence and so I plan to purchase this home with that type of loan. 

If you don’t have a primary residence you are in a good position to house hack.

My issue has been that every bank and credit union I've contacted has stated that the home needs to be my primary residence in order for them to consider a HELOC.  

So, can you tell me your type of loan, like:traditional mortgage types (FHA, VA, conventional)hard moneycommercial mortgage (like a portfolio loan or secondary market commercial)private moneyHELOC Seller financingPersonal savingsIf you did a BRRRR deal, you can list both the purchase and refinance source.And if it was a traditional mortgage, hard money, or conventional mortgage - what company did you use to originate the loan?

Oh, that a primary residence mortgage application could be so easy...On a separate note, the other two said they would only lend business to business. 

I recently sold my primary residence in Phoenix, and I am planning on turning that gain into my next real estate investment. 

This is my primary residence, so it doesn't currently qualify for a 1031 exchange but I'm looking into making it a rental and what that would look like.