The Daleks operated Exterminator class flagships during the Second Dalek War. The Exterminator was commanded by Dalek X, the Dalek Inquisitor General. (PROSE: Prisoner of the Daleks) The Dalek Emperor's flagship was present at the Fall of Gallifrey. When the Doctor displaced the planet and the Dalek Fleet annihilated itself, (TV: The Day of the Doctor) the flagship fell through time, winding up in the solar system during the reign of the Fourth Great and Bountiful Human Empire. The flagship led an invasion of Earth in 200,100 before it, and the rest of the Dalek force, was destroyed by Rose Tyler. (TV: The Parting of the Ways)
The Imperial Flagship served as the personal vessel of Emperor Ludens Nimrod Kendrick Cord Longstaff XLI. (TV: Nightmare in Silver)
Cyber-Flagships were the leading vessel of a Cyber-Fleet, commanded by a Cyber-Leader. One Cyber-Flagship led the Cyber-Fleet in an attack on Nomicae in the 5320s. It was destroyed by the Harrigain. (COMIC: The Bidding War)
During the Dalek-Movellan War, the Movellan flagship abducted the Tenth Doctor and Davros on Kembel. Seeing a chance to destroy the Movellans, Davros attempted to upload a computer virus into their network only for the Doctor to briefly sever the flagship's connection to the Movellan network, halting the spread and allowing the flagship to purge the malicious code. (AUDIO: The Triumph of Davros)