(I apologize for the delay in getting this out: I can't do NaNoWriMo and Pokedex at once.)
Although Blaziken are unable to fly, this has not stopped them from preying on the food sources of their flying ancestors: small birds such as Taillow and flying bugs such as Beautifly. It is their method for doing so which is most remarkable: rather than climbing trees to prey on nests or relying on ranged attacks to hit these inevitably distant targets, Blaziken jump high enough into the air to knock out their foes in mid-flight!
This is not the only use for a Blaziken's remarkable jumping ability. In the old days, they were used as a measuring stick for religious buildings in Hoenn, whose builders often tried in vain to create structures so tall no earthly creature (which in this case meant a Blaziken) could jump over them, which was thought to honor the gods. In time, theologians solved this problem by declaring Blaziken not earthly creatures, but a type of bird, because of their avian roots: although Machop can clear some small skyscrapers even today, they were (and remain) far weaker jumpers.
Today, Blaziken are often found jumping from rooftop to rooftop in contests of agility hosted in major cities. These contests are not especially profitable, and most trainers view them more as a training exercise than a sport in their own right, for Blaziken depend on their control of their jumping in combat. It does maintain a small following of avid fans, however, and has often been used as inspiration for exciting chase scenes in film and levels for platform video games alike.