pathfinder 1e – Does hideous laughter make a flying foe prone and cause the foe to fall?

Pathfinder creative director James Jacobs addresses whether or not a flying creature can be rendered prone in this 2012 exchange:

Can a creature… with natural or magical flight be knocked prone?

Not when they’re flying. You can mess with a creature in the ways detailed in the Fly skill, which might make them fall, but you can’t make a flying creature prone. Or a swimming or burrowing or climbing creature, for that matter.

Absent this pronouncement, the GM determines the effect of rendering a flying a creature prone. Note that flying creatures were already immune to the trip combat maneuver (which, when successful, often results in a prone foe): “Some creatures—such as oozes, creatures without legs, and flying creatures—cannot be tripped.”

Creature that fly without wings usually stay aloft even if they can’t take actions

As per this question, a creature that’s flying without the use of wings (like a witch employing the hex flight to use an effect like the spell fly) doesn’t fall from the sky even when it gains the condition paralyzed: “A winged creature flying in the air at the time that it becomes paralyzed cannot flap its wings and falls,” yet creatures that fly winglessly go unmentioned and therefore are unaffected.

Since the spell hideous laughter inflicts upon the subject a condition substantially less restrictive than the condition paralyzed, the unfortunate witch will still be unable to act but likely won’t plummet into her own black tentacles.