I - Rules
(see JITD, p. 22; FAQ, p. 5-6)
Figures with the Fly ability may move through enemy figures and obstacles as if they weren't there. However, flying figures cannot end their movement in a space containing another figure or an obstacle that blocks movement. A flying figure may end its turn in a space containing an obstacle that inflicts damage without effect.
Fly vs Grapple
A figure with Grapple affects flying units. However, it would not affect a soaring figure.
Fly vs Aura
Figures with the Fly ability are affected by the spaces around an enemy with Aura but not the space where the enemy figure stands. The FAQ states that a flying monster passing through a hero that has Holy Aura, does not suffer a wound for the space it “shares” with the hero.
II - Reference
Heroes with the Fly ability: Zyla.
Feats granting the Fly ability: Carried By Air (only 1 turn).
Items granting the Fly ability: Wings of Regiroth.