WebcamStudio allows you to run several effects at once, between other interesting features like running images, videos and other stuff as your webcam in order to be streamed in almost any via (web service, video conferencing system, chat, etc.)

In the next screenshot I am using my webcam in order to show the images flipped horizontally (up to down), but you can both invert horizontally, vertically and to run several effects at once.

Note: I am using Cheese in order to preview the webcam's output.

Aditionally you may wish to take a look at this answer by @Veazer: https://askubuntu.com/a/124934/9598 Posted here for your convenience:

I think you'll need to create a launcher script for each application
that needs this fix. For example, if you wanted a script for Skype
that flips the video horizontally this should work:

#!/bin/bash

export LIBV4LCONTROL_FLAGS=1 && LD_PRELOAD=/usr/lib32/libv4l/v4l1compat.so skype

If the image is not flipping correctly, try different values for
LIBV4LCONTROL_FLAGS. My camera requires a vertical flip so I use '2'.
I haven't used this on 11.10 until today when I saw your message, but
it seems to be working.

No working for me but @Luis Alvarado informs that it works, if this last one is working for you please don't forget to give credit to its author.

Good luck!