Just like a normal player, pet movement speed while flying would be higher than land. The speed would vary depending on the spirit type.

Additional speed would be increased accordingly to the buff applied on the spirit. The max flight speed for a spirit is 1.6.

Skills which affect flying speed:

Armor Spirit
For 5 minutes, Spirit's patk and matk +40%; All elemental defence +10%; Magic boost +400; Movement speed +30%; Magic Accuracy +1000; Accuracy +1000.
Mana consumption: 400
Cast time: 1 sec
Cool down: 5 min

Spirit Armor of Darkness/Light
In 10 minutes, Spirit Magic boost +640; Attack speed +10%; Movement Speed +10%; Pdef +13%; Patk and Matk +85%; Recover 110 HP every 6 sec.
DP Consumption: 2000
Cast time: 1sec
Cool down: 30 sec

Pet Speed Chart:

Earth
Land unbuffed: 7.0
Flight unbuffed: 10.0
Flight (DP buff): 11.0
Flight (Armor Spirit): 13.0
Flight (DP + Armor Spirit): 14.0

Water
Land unbuffed: 8.0
Flight unbuffed: 11.0
Flight (DP buff): 12.1
Flight (Armor Spirit): 14.3
Flight (DP + Armor Spirit): 15.4

Fire
Land unbuffed: 8.0
Flight unbuffed: 11.0
Flight (DP buff): 12.1
Flight (Armor Spirit): 14.3
Flight (DP + Armor Spirit): 15.4

Wind
Land unbuffed: 11.0
Flight unbuffed: 14.0
Flight (DP buff): 15.4
Flight (Armor Spirit): 16
Flight (DP + Armor Spirit): 16

Magma
Land unbuffed: 10.0
Flight unbuffed: 13.0
Flight (DP buff): 14.3
Flight (Armor Spirit): 16
Flight (DP + Armor Spirit): 16

Tempest
Land unbuffed: 12.0
Flight unbuffed: 15.0
Flight (DP buff): 16
Flight (Armor Spirit): 16
Flight (DP + Armor Spirit): 16