My colleagues Chris Organ and Andrew Shedlock, who provided evidence that theropod dinosaurs already had (somewhat) reduced genome sizes prior to the evolution of birds (Organ et al. 2007) have followed up their study by estimating the genome sizes of several species of pterosaurs.

Pterosaurs were the first vertebrates to evolve powered flight, having taken to the air 70 million years before birds and 150 million years prior to bats. Interestingly (though perhaps not surprisingly at this point), they seem to have possessed reduced genome sizes, and these downsizings of DNA amount began before flight arose.

On the other hand, it is clear that the estimates for non-avian dinosaurs are not as small as modern birds and that the estimated ancestral genome size for birds larger than the genome seen in various groups. Patterns can be observed in terms of flight ability across living avian species. Notably, my student Chandler Andrews showed that genome size is correlated with wing loading (and indication of flight capacity) within perching birds, and we are currently writing up major projects on bird groups with different flight ability as well as a study of hummingbirds; Jill Smith, another student, also has a large bat study to write up.

The story thus seems to be that genome reduction occurred in the dinosaur lineage of which birds are descendants before flight (so did feathers, bipedalism, and other characteristics), but were later further adjusted when flight arose (as were feathers, etc.). The same reductions before flight probably occurred in the pterosaur and bat ancestors. So it's not flight per se that matters, but a feature linked with flight.

As Organ and Shedlock put it, "we hypothesize that a metabolic intensity required for flight, not flight itself, explains the correlated evolution between genome size and flight in amniotes." -- this seems very plausible given the growing amount of data on this topic.

References

Andrews, C.B., S.A. Mackenzie, and T.R. Gregory. Genome size and wing parameters in passerine birds. Proceedings of the Royal Society of London B, in press.

Organ, C.L., A.M. Shedlock, A. Meade, M. Pagel, and S.V. Edwards. 2007. Origin of avian genome size and structure in non-avian dinosaurs. Nature 446: 180-184.

Organ, C.L. and A.M. Shedlock. 2008. Palaeogenomics of pterosaurs and the evolution of small genome size in flying vertebrates. Biology Letters, in press.

Zimmer, C. 2007. Jurassic genome. Science 315: 1358-1359.