Yes, he can.
FlyingDDI is a form of movement that leverage the fly speed, but is not limited to straight lines. In fact, you can take the walk, shift and running actions when flying.
Flight follows the basic movement rules, with the following clarifications.
Fly Speed: To fly, a creature takes the walk, run, or charge action but uses its fly speed in place of its walking speed. A creature that has a fly speed can also shift and take other move actions, as appropriate, while flying.
Moving Up and Down: While flying, a creature can move straight up, straight down, or diagonally up or down. There is no additional cost for moving up or down.
Falling Prone: If a creature falls prone while it is flying, it falls. This means a flying creature falls when it becomes unconscious or suffers any other effect that knocks it prone. The creature isn’t actually prone until it lands and takes falling damage.
Remaining in the Air: A flying creature does not need to take any particular action to remain aloft; the creature is assumed to be flying as it fights, moves, and takes other actions. However, a flying creature falls the instant it is stunned, unless it can hover.
Landing: If a creature flies to a surface it can hold onto or rest on, the creature can land safely.
Terrain: Terrain on the ground does not affect a flying creature if the terrain isn’t tall enough to reach it. Because of this rule, flying creatures can easily bypass typical difficult terrain, such as a patch of ice on the ground. Aerial terrain can affect flying creatures.
The term falling was previously defined as crashing.