Bitcoin miners have no role here. Anyone can sign up to be a Stack-miner by bringing in their own BTC into this network. That amount (in BTC) is distributed to those who have staked their Stack-tokens. A pRNG process (based on VDF or VRF) selects one of these miners at random to create the next block

Source: https://blog.blockstack.org/realizing-web-3-proof-of-transfe...

Edit: typo