Yes—many bird photographers consider a Canon 7D-series body with the EF 400mm f/5.6L a strong, cost-effective birds-in-flight setup. The 400mm f/5.6 is widely regarded as light, very sharp, and well suited to fast AF tracking in good light.

However, your FZ1000 already gives a similar angle of view at the long end: its built-in lens is about 432mm full-frame equivalent, while a 400mm lens on Canon APS-C gives a narrower field of view (about 640mm equivalent). So you would gain more framing reach, and likely better AF/lens performance, but not a dramatic jump in “zoom” compared with the numbers printed on the cameras.

The 100-400mm zoom is more flexible, but the older version is generally not considered as strong optically or for AF as the 400mm f/5.6 prime. Image stabilization helps with camera shake, but for birds in flight you’ll often be using very fast shutter speeds anyway.

Your concern about finding birds with a 400mm prime is valid, but it improves a lot with practice. Many photographers train on larger, predictable birds like ducks or gulls to build the muscle memory needed to get on target quickly.