They should be able to help facilitate this for you.

The purchase price is released to escrow immediately, while the remaining funds for material costs and labor are disbursed to the general contractor in stages to facilitate the completion of the renovations.

I did not use the funding directly to pay for a property or rehab but it did help "facilitate" the ability to safely and successfully perform a BRRR.

Food for thought: General concensus is double closings are not illegal.Full disclosure must be given to all parties.IMO (and Im a rookie): There is a good chance that in the near future attorneys (representing sellers) will begin going after realtors that "facilitated" double closings because they (sellers) will realize they they are on the hook for the bank's loss including the "profit" the investor made in the flip.

Can I use my Traditional IRA to facilitate something like that?

Your rockstar doesn't control how fast or slow the old lender (who is no longer getting paid for their work to-date on this transaction...) helps facilitate. 

My plan is to use HML to facilitate the out of state purchases while sitting on the profits of the sale of the CA property.

It exists to facilitate discussion between investors so that we may all collectively IMPROVE. 

As I have an FHA loan, there is a mandatory partial claim to facilitate the back end repayment.  

@Chris Jensen could you help explain how you would use a HELOC to facilitate BRRRR?