@Account Closed
Yes, in the BRRRR model, your "refinance" will pay off the initial acquisition loan, renovation costs, and down payment, thus returning all of your initial capital invested. Ideally, the refinance gives you even more money back than you put in. Regardless, you then take the capital that you got back from the refinance, and look for more properties and "repeat."
The BRRRR model doesn't imply that you need to pay off the ending refinance and mortgage before you "repeat." Typically, the refinanced property keeps a mortgage on it and it's paid off through the term of the loan via amortization (likely 30yrs.) You can always make additional principal payments with the cash flow from the rental and more aggressively pay down the mortgage if that's best suited for your investing goals & strategy. With today low rates, it's not necessarily a bad thing to have a mortgage on the property, plus there's tax benefits.
As for cash flow.....yes, in the BRRRR model the plan is to make sure that your rented property pays for it's mortgage payment, taxes, insurance, and gives you additional cash flow on top of these expenses.
Hope this helps!