I've used trampolines and HJ mats for training of injured athletes but I don't think I'd really find it all that useful for healthy athletes. They would definitely increase hip flexor strength (or endurance) if used as in that video but I really don't see this as a limiting factor in sprint performance. In fact, the tramps would reduce demand on the factor that I believe does most limit sprint performance (vertical ground reaction force) while placing a higher load on the musculature which is not a limiting factor (hip flexors).
There's a time and a place for tramps but I wouldn't make them a major point of emphasis in your training because you'll be training muscles of secondary importance (hip flexors) and placing little emphasis on the muscles of great importance (hip extensors).
Mike, this exercise does not load the hip flexors excessively in my opinion. The only places I've ever felt fatigue from it was in the quads, hips, hamstrings, and calves and while my rectus femoris may have been fatigued, it was not more so than any place else.
As for it not training vertical ground reaction forces (the limiting factor in sprint speed), it indeed does, but indirectly. Tramp sprints are used as a low impact way to train the anaerobic glycolysis energy pathway. And a greater number of glycolytic enzymes present in a muscle, the higher potential stiffness that muscle has. When combined with other, higher impact, methods of training, tramp sprints are a useful tool.