How do I fake accent?

Now, as a non-native speaker, I naturally have this weird accent that somehow pops up sometimes among my tv-show influenced bland vanilla american accent.

The question is, how to fix that - and has anyone tried "learning" another accent? Might be cool to pretend you're an Australian sometimes.

I've lived in Scotland all my life, and I can't do a Scottish accent.

Is this going to make it harder to pick up foreign accents?