Flash Player doesn't detect my IP Android Webcam

Flash Player only knows about webcams exposed via DirectX (I'm assuming we're talking Windows).  If it's not listed, it's because the operating system isn't exposing it to us as a relevant device.  This happens for some high-end conferencing camera setups a well.  A commodity USB webcam is your best bet for the typical cam chat site.

If you're using it for conferencing or broadcasting and have options beyond Flash Player itself, you could use something like the free Flash Media Live Encoder for broadcasting on more esoteric configurations beyond basic commodity webcams.

media encoder, video capture software, audio capture software | Adobe Flash Media Live Encoder