A lot of shows like Xena protray the hero doing flips (forwards or backwards) to catch up to a running villian who has 100m or so lead. Can just by flipping actually catch a runner? Is it a fast and efficient way of covering ground?

No. Running is faster.

Otherwise, the Olympics would have the 100m flip instead of the dash.

agreed: flipping does not accelerate the person, it just looks cool on TV