Some devices with Kitkat can be found with Permission manager in Settings. If it is enabled and an app asks for a permission that the manager is required to scrutinize, you might have inadvertently blocked it, or could be default block for certain apps.
To ascertain that Skype is denied the Camera permission or not, go to
Settings -> Security -> App permission. Your device might have another name for it but possibly should be at similar location. See if its enabled or not. The situation might also be similar to questioner's:
Turns out Skype was on
Always deny... Interestingly,
App Permissions in Security was grayed out while ON! I had to turn it off first, which got me a security warning that I am going to lose manual control over apps. I proceeded with Yes anyway, then turned it ON again, and only then I received the familiar list of permissions to control.
It its enabled or similar to the one mentioned above, then either disable it or find your app into it and change the camera permissions.