Flush or Bleed to fix long brake pedal travel

[sip]

I parked my 2009 Mazda 3 in the past two years to save insurance (I have two vehicles). Today, I replaced all 4 pads and rotors because the brakes were spongy and depressed too much. Initially,my mechanic thought the brake cylinder has failed but later when he removed the wheels, he found the brakes have seized, so he replaced the all 4 pads and rotors. He didn't replace the calipers, so I assume he unseized them.

The problem is even after the new brake job, the brake pedal travel too much. I want to bleed the brakes to get rid of air (to see whether this would stop the long brake pedal travel). Is flushing the brake fluid as effective as bleeding to get rid of air? If so, I rather do a flush than a bleed.