I don't know if you've spoken with a physician about attempting to improve your respiratory capacity/efficiency, but that's the best place to begin. I would suggest seeing a pulmonologist to get a baseline, prognosis, and treatment plan that is individual to you and your malady.
I don't know if this is the case for all of the uniformed services, but the Army regulations state:
Asthma that has a Forced Expiratory Volume-1 < 50% of predicted despite appropriate therapy, that has required hospitalization in the past 12 months, or that requires daily systemic (not inhaled) steroids. Asthma that has been well controlled for 6 months and is evaluated to pose no risk of deterioration in the deployed environment may be considered for waiver.
As far as I know, there is no way to game a pulmonary function test, and I don't think it's a good idea to do so anyway if you're looking to join the service. The last thing you want is to put either yourself or your comrades in harm's way due to a foreseeable and entirely preventable episode.
In any case, if you do end up not seeing a physician and begin a program on your own, start extremely slowly in regards to respiratory and cardiac demand and work your way up in very small increments. Maybe steady-state cardio is the best thing, so you can easily control the variables.