They're impressive live. definitely put on a good show. Her voice has been incredible, every time I've heard them. Have you heard the 'baby-boom' stuff they did too? it was like an acoustic side project. Worth a listen.
I reckon something like adidas ZX90s RUN would be pretty well suited. Lightweight, very breathable, flexible sole, very grippy. Don't know though, because I've never tried freerunning.
Air max 95's? edit: I hate these with a passion anyway, but wouldn't the sole be way to thick for parkour stuff? Would a lightweight running shoe be much more appropriate?