This works exactly like the native version of docker-squash so familiarize yourself with it's docs at https://github.com/jwilder/docker-squash.
The main difference is you'll need to swap out the sudo docker-squash command for docker run -v /tmp -i myyk/docker-squash and optionally add volumes for you inputs/outputs.
So if before you had:
$ docker save <image id> > image.tar
$ sudo docker-squash -i image.tar -o squashed.tar
$ cat squashed.tar | docker load
$ docker images <new image id>
Now you'll have:
$ docker save <image id> > input/image.tar
$ docker run -v $(pwd)/input:/input -v $(pwd)/output:/output -v /tmp -i myyk/docker-squash -i input/image.tar -o output/squashed.tar
$ cat output/squashed.tar | docker load
$ docker images <new image id>
I've confirmed this works from OS X (Yosemite) with docker-machine and from Ubuntu (Trusty).