This is not defined within the game rules.
As far as I know, there is no explicit rule on this exact issue within the 3.5 core rules.
How exactly a Prone creature's land movement is hampered is not even defined. Using a legalistic definition, I can not see anything that, say, prevents Running while Prone, nor anything about a Prone creature needing to (or being able to) crawl. As far as I can tell, people just assume this due to the names of the conditions (and rightly so, in my opinion). There's a limit to how defined we can demand the 3.5 rules to be.
Here's what I can infer on the subject of Prone creatures flying.
I'd say no, a creature that has the ability to fly but has been tripped can not fly away without first standing up.
This is because the following is a part of the description of a character being Prone: "The character is on the ground". I'd argue that a character that is "on the ground" can not make use of special options relating to flight.
However, it is not so easy getting a creature that can fly to be Prone to begin with, as Tripping has a special effect on flyers rather than rendering them Prone. See page 145 of the Rules Compendium:
Tripping a Flying Defender
A winged creature can be tripped, and if it is, it falls as if it didn't maintain its minimum forward speed.
As for whether Prone creatures have special uses for their move action other than crawling and standing up - no. Once again, nothing is defined.