A polishing system and method for polishing a channel formed within a component is disclosed. The polishing system may include a tooling element operable to be positioned within a recess formed partially through a component. The tooling element may include an outer surface having a geometry corresponding to a geometry of the recess formed in the component. The tooling element forms a channel between the recess of the component and the tooling element when positioned in the recess. The system may also include a first member in fluid communication with a first opening of the channel, and a second member in fluid communication with a second opening of the channel. The second opening may be in fluid communication with the first opening via the channel. Additionally, the first and second member may be configured to continuously vary a pressure within the channel to move an abrasive slurry within the channel.