Wings of Air (Sylph)
The winds lift you, carrying you where you want to go.
Prerequisites: Airy Step, character level 9th, sylph.
Benefit: Your bonus on saves against effects with the air or electricity descriptors and effects that deal electricity damage increases to +4. In addition, you gain a supernatural fly speed equal to your base speed (good maneuverability). You may only fly with this ability when wearing light armor or no armor.
Question: Does monk fast movement boost the fly speed granted by this feat?
Fast Movement (Ex)
At 3rd level, a monk gains an enhancement bonus to his land speed, as shown on Table: monk. A monk in armor or carrying a medium or heavy load loses this extra speed.
I'd say no. It's written specifically as an increase to Land Speed and not Movement Speed or modes of movement.