FLY: The American Sign Language (ASL) sign for "fly"

Also see: PILOT

Use the "I love you" handshape to represent an airplane flying through the air.  This sign is a noun/verb pair. Note:  You might want to angle your palm a bit more downward than I'm doing here.

Sample sentence: YOU FLY BEFORE YOU?

For "AIRPLANE" use a small double motion.  You move the hand forward just a couple inches or so, then bring it back, then move it forward again.

BIRD-in-flight 
Or FLYING-bird:
Once you have established that you are talking about a bird, you could then show that bird in flight.

Note:  If you want to talk about how a bird is flying, you can flap your arms/hands as if you had wings to show what kind of wing strokes the bird is making.
For a small bird you would flap just your hands or for a very small bird you could "flap" the index and middle fingers of your hands (while making a whistling facial expression).  For a large bird or a pterodactyl you would extend your arms and use a large flapping motion.
For a bird with a broken wing you could just flap one arm or hand.
For a penguin you'd hold your hands down near your hips, (touching your wrists to your hips and pointing your fingertips out to the side) then do a side to side rocking movement in your torso to represent the waddling of a penguin.

Sample sentence: every-YEAR AUTUMN-[fall] BIRD FLY-[flap-wings] SOUTH.

Another way to show this concept is with FLY as in GLIDING BIRD:

Or FLY as in FLAP WINGS:

FLYING-(insect)  "buzzing"
You can can show how an insect (such as a fly) flies:

Some types of FLIES:

FRUIT FLY:

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SAND FLY:

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HORSE FLY:

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DRAGON FLY:

Version 1:

Version 2:

Notes: 

Also see: PILOT
Also see: FLY-(insect)

Also see: AIRPLANE

Also see: FLY-flapping