If you need cash to buy your next house get a HELOC in place before you move out while it is owner occupied. 

I was able to get a HELOC on the first one for 90K because it was a condo in Florida and doubled in value (has since crashed). 

Texas is okay but higher taxes and can't get a HELOC. 

Whatever I do, I would need to do with a HELOC—effectively financing 100% of the property (down payment and closing financed with HELOC, rest of purchase financed with a mortgage). 

If you take a HELOC at home, I'd imagine you'd be able to cover that cost as well.

I’m trying to get a heloc or cash out refi on a primary residence duplex.l under FHA.I have great credit but modest incomeWife has bad credit with better income therefore I don’t believe we will qualify for heloc.Our plan was to get heloc to use as a down payment on another house hack or general investment property.So far our mortgage company said they could do the cash out refi which would raise our mortgage from $800 to $1200 (current rate is 3.62) and the rate would go to 6.6To pull out hopefully 30-35k maxMy concern is if I do the cash out.

I'm a fan of using HELOC or LOC if you have the equity.

The more traditional way, assuming you actually have adequate equity in your rental, is to take out a HELOC on the rental. 

Finance was a combination of a few different vehicles and ultimately ended with a HELOC which was then used to fund multiple other projects over the years.

I would find other ways to pay off the HELOC - even if you have no cash flow temporarily.