Having seen its wild ancestors, the Burmese fowl, also called the northern red jungle fowl, all over India and Bali, I can confirm that these birds fly, and quite well.
From the theatlantic.com
The grey and red jungle fowl have, at present, disjunct ranges, but that may be a product of recent ecological changes, including human alterations of habitats.
From the scienceblogs.com
They studied how individual patterns of gene activity in the brain were different for modern laying chickens than the original form of the species, the red jungle fowl.