In the case of FLX stakers, the RAI that accrues for them is auctioned in exchange for FLX. The FLX proceeds from the auction are then sent to the staking pool.
As for buyback and burn, RAI is first accrued in the protocol's balance sheet. Once there's enough RAI in the balance sheet, the protocol can start to auction some of it in exchange for FLX that is then burned.