I know I've read on here of accounts of folks refinancing multiple properties they already own into a single portfolio loan, but I don't know if that's different than trying to do so at the time of purchase.

There is no seasoning for rate & term refinancing.

I am trying to learn this whole brrr strategy, and I am stumped on the refinancing part If I was to get a hml and do the buy, Reno, rent.

Live in it for a year to meet the primary residence rule, make the cosmetic repairs to force equity, then look into refinancing out of your VA loan into a conventional loan, so you can use your VA loan again. 

Your only risk would be rising rates, which may not make it worth refinancing after 2 years.

It has to do more with refinancing or selling.

Hey Gang, I'm looking to get some properties refinanced.

I took some SWAG guesses on doing this BRRRR with Hard Money and then refinancing with a Conventional loan.

Bought a 6 flat, full gut ($700k rehab), rented it out, refinanced, and rolled proceeds into another project.

When refinancing you can wrap the closing costs into your loan amount, assuming there is enough equity.