Hi Andrew. Here is a web site which shows some theories on how flight evolved in birds. It may have nothing to do with predators:
The selective pressure on the pre-birds to evolve the ability of flight in the sense of elevation, most likely was the reduction of the damaging impact of a jump or a fall from a level, supposely from the side of a tree-trunk.
(I surmise they use the term "Pre-bird", since "ProtoBird" TM has already been patented.)