I appreciate the advice and keep up the great work on BP Money, really enjoying the podcast =). 

Not having access to these (which the owner in the scenario DOES enjoy) leaves you with cashflow - but with very little in the way of knobs, dials and levers with which to manipulate the factors that influence cashflow... 

Better to build your own equity through the debt pay down, enjoy the tax benefits of ownership, and garner the equity of an appreciating asset.

I’ve been told that banks in TX are not able/willing to do a cash out refi on investment properties.

Real estate investing is a pretty forgiving world and the average person can still make money even with some pretty big mistakes.Buckle in, keep your arms and legs in at all times, and enjoy the ride!

Chris -   some lenders  will not let a HELOC in 1st position.....so watch for this …...most lenders  will not do helocs on  investment  property only on primary residences  ( there may be some exceptions )   …..if these have 2 adjacent tax lots - you prob wont find a lender to lend one loan on both  properties  …..I would recommend  checking with the smaller banks and cedit unions in your area ( n Pierce / s King counties ) good luck

Does anyone know of banks (or if it is even possible) that would appraise a 1-4 unit rental property based on cashflow?

Here's my personal story of a 203K / HomeStyle Renovation I did: https://www.biggerpockets.com/member-blogs/12390/86740-my-experience-with-a-203k-homestyle-renovation Enjoy!

Can I use someone else's money (that wasn't gifted or loaned to me) for my down payment on a bank loan?  

They are non-banking investors looking for someplace to invest their money.