No, the half-celestial barbarian uses it's racial speed to determine air spead.
Yes, the half-celestial Monk gets the enhancement to fly speed speed.
Speed
A half-celestial has feathered wings and can fly at twice the base creature’s base land speed (good maneuverability). If the base creature has a fly speed, use that instead.
Fast Movement (Ex)
A barbarian’s land speed is faster than the norm for his race by +10 feet. This benefit applies only when he is wearing no armor, light armor, or medium armor and not carrying a heavy load. Apply this bonus before modifying the barbarian’s speed because of any load carried or armor worn.
Fast Movement (Ex)
At 3rd level, a monk gains an enhancement bonus to her speed, as shown on Table: The Monk. A monk in armor or carrying a medium or heavy load loses this extra speed.