Refinancing a rental And using the cash out to purchase another property.  What would my tax implications be in 2 years if I then sell the refinanced property

You refinance rental A to obtain $50k (example) cash. 

You use that $50k to buy rental B. 

The interest on the $50k portion of that refi is deducted against rental B. (IRS interest tracing rules)

When you then sell property A- you pay back the full loan. And now there is no more interest to deduct against property B.

Your financing has Zero effect on the the gain when selling a property....it makes no difference if you borrow it all, or pay all cash....profit is sale price (less actual selling cost) minus basis, regardless of financing or how much cash you receive at closing.