I recommend you talk to a lender and get real clear on what you can qualify for, what you can do to improve your borrowing position, and make sure you have your finances under control.

We are able to borrow the money at 5%, however the lender also wants a small portion of cashflow (not equity) from each property we buy.

A Veterans Administration mortgage where a Veteran and non-Veteran co-borrower qualify for a mortgage together is called a joint VA loan.But like I said to Denis some lenders do not offer this options due to guide lines or investor overlays. 

Your best bet is to borrower the downpayment (although, if your property doesn't debt service, you won't cash flow)

My product is slightly different, it's more about connecting borrowers to lenders, so I don't think I need to learn about Fannie Mae at this point.

When he goes to refinance they’ll only borrow him $360k. (80% of the value.).

Hi VA loans are originated based on the entitlement amount of the borrower.

I paid cash, but borrowed 30k from a family member to cover some extra costs and renovation, the HOA fee is $135, and I pay my family member $500 a month until the 30k is paid off.

How much would you need to borrow? 

I'm a strong borrower so can likely buy up to 4M.