There is more information available on this subject at Flagship on the English Wikipedia.

The UNSC Infinity, experimental flagship of the UNSC Navy.

A flagship is a warship used by the commanding officer of a fleet or battle group. It can be any warship and is not restricted to any particular classification; however, it is typically one of the largest ship types within the fleet, such as a cruiser or a carrier, even an orbital platform. The purpose of a flagship is often for command and control.

Flagships in the UNSC tends to be cruisers or carriers. Although, in smaller fleets, a frigate or destroyer may be the flagship. In the Covenant fleet, flagships tend to be CCS-class battlecruisers or CAS-class assault carriers in the typical fleet. However, in battle groups, the flagship may be a cruiser or, rarely, a destroyer. In particularly large and important fleets, the flagship may even be a CSO-class supercarrier.

Known flagships

Covenant

Seeker of Truth leading its fleet at Alpha Halo.

• Ascendant Justice: DDS-class carrier
• Doctrine's Command
• Incorruptible: ORS-class heavy cruiser
• Long Night of Solace: CSO-class supercarrier
• Seeker of Truth: CAS-class assault carrier
• Shadow of Intent: CAS-class assault carrier
• Song of Retribution: CAS-class assault carrier
• Sublime Transcendence: CSO-class supercarrier
• Truth and Reconciliation: CCS-class battlecruiser

UNSC

• UNSC Forward Unto Dawn: Charon-class light frigate
• UNSC Trafalgar: Punic-class supercarrier
• UNSC Hopeful: Mobile battlefield hospital
• UNSC Leviathan: Marathon-class heavy cruiser
• UNSC Canberra: Marathon-class heavy cruiser
• UNSC Pillar of Autumn: Halcyon-class light cruiser
• UNSC Everest: Valiant-class super-heavy cruiser
• UNSC In Amber Clad: Stalwart-class light frigate
• UNSC Infinity: Infinity-class supercarrier
• Cairo Station: Orbital defense platform

Forerunner

• Mantle's Approach: Unknown class