Follow along with the video below to see how to install our site as a web app on your home screen.
Note: This feature may not be available in some browsers.
Version 2.1.0.46
actually I just saw that "enable video calling" was not checked.
I will try and see if this works.
You can not use the version from the market, there is another version that you need to use instead. I know I found a link on a thread in this forum, just can't remember which one and I think it was over at XDA where they had the apk you would need.

I got Skype to work with video on my Droid Bionic by doing the following:
1 Uninstall all Skype versions on your phone.
2 Install the modified version of Skype found here xda-developers - View Single Post - Skype 2.1.0.46 (v11) / fixes, extra features & more!
3 Sign in to Skype and on the main page hit the menu key (on your phone) then go to Advanced Settings.
4 Check-mark the option Use valid preview surface
5 Once back and on the Skype main screen hit the menu key (on your phone) and go in to Settings (Regular Settings this time) and check-mark Enable video calling
Enjoy your video calls on your phone.
I have tested this on mine and it works Phone to Phone or Phone to PC. Both cameras are working.
Credits go to theos0o from XDA developers and gazan1204 from droid forums