10k is a great start! Kudos to you!
Keep in mind that when doing a BRRRR, eventually you are going to have to go to a lender to execute the refinance. In fact, I would START with finding a lender and explain to them what you are planning to do. Spell it out for them best you can. You do not want to get into a deal and then start reaching out to lenders only to discover none of them will lend on the deal.
Most lenders are going to require you have 3-6 months PITI (Principle, Interest, Taxes, Insurance) in the bank in order to qualify for the cash out refi. While you might be able to generate enough forced appreciation with a rehab, you'll likely being borrowing funds from a hard money lender to cover the cost of the initial purchase, the rehab, and the holding costs.
Not saying this can't be done, but you may have to get creative. Do you have access to any sort of line of credit like a HELOC? That's how we funded the purchase of two BRRRRs.