Chocobo Riding time is set at 15 minutes for levels 15-19, and from 20+ it's set at 30 minutes. Each +1 you receive from gear adds an additional minute to your chocobo riding time, however such gear has no effect below level 20.

Name Level Slot Info
Chocobo Boots 1 Feet  Chocobo Riding Time +3
Chocobo Gloves 1 Hands  Chocobo Riding Time +3
Chocobo Hose 1 Legs  Chocobo Riding Time +4
Chocobo Jack Coat 1 Body  Chocobo Riding Time +5
Chocobo Wand 1 Weapon  Extends Chocobo Riding Time (+30)
Orange Racing Silks 1 Body  Chocobo Riding Time +10
Rider's Boots 15 Feet  Chocobo Riding Time +3
Rider's Gloves 15 Hands  Chocobo Riding Time +3
Rider's Hose 15 Legs  Chocobo Riding Time +4
Rider's Jack Coat 15 Body  Chocobo Riding Time +5
Chocobo Torque 81 Neck  Chocobo Riding Time +4

The gear listed above does not extend the time for a personal chocobo. The only way to increase the riding time of a personal chocobo is achieved by wearing the Red Racing Silks when using the Chocobo Whistle.