I traveled to Jackson again yesterday, and had the pleasure of encountering these juvenile trumpeter swans. The trumpeter swan is North America’s largest flying bird. Although not listed as an endangered species, trumpeter swan populations were decimated in the past and have made a long, slow return to healthier numbers, with western Wyoming’s Green River basin becoming a key area for this expansion.
Biggest flying bird as in wing-span? That's a big bird! What about California Condors?
Biggest as in all over– they weigh more than eagles. Andean Condors and wandering albatrosses have bigger spans, and a couple of the biggest bustards and eagles may weigh more.
Check out this photo at TetZoo:
http://scienceblogs.com/tetrapodzoology/bald-eagle-attacks-swan-photographer-unidentified-but-not-hoax_Jan-2010.jpg
I think you falconers would like it.
That should give you an idea of how big a Trumpeter swan is.
I thought the great bustard, which now breeds on Salisbury Plain (http://10000birds.com/the-salisbury-plains-great-bustards.htm) was the largest flying bird.