Manycam is a webcam software for Omegle, though many people have had a really tough time setting it up!
In Omegle, choose the “allow” option in the Adobe flash popup window, then “camera” dropdown list that appears.
Choose “ManyCam virtual webcam” or “Manycam Video Source.”
You might also have to select it as an audio input, too.
See also: Omegle nudity: Is it allowed or not?