When you shoot a bird in flight, you are shooting a rather dark object(*) against a light background, so general exposure rules hardly apply.

Using auto-exposure is better (this takes in account changes in orientation from the sun or passing clouds), but with a 200mm the bird must be a rather tiny part of the picture so the camera mostly exposes for the bright sky in the background and the bird is under-exposed.

The solutions:

1. Set you camera to use "spot" metering, so that the camera computes the exposure from a small centered part of the frame. This reduces the influence of the background. Problem: your bird has to be there at the center when you take the shot, otherwise your camera will expose for the sky. So this requires a very accurate aim for a bird in flight.
2. Keep the standard "weighted" metering, but use exposure compensation to overexpose by about one EV (or more if necessary, after checking your first few shots).
3. If you shoot "raw" you can recover some of the under-exposure in post-production (the necessary data will have been lost if you only have the JPEG). One limitation is that you may want to use burst mode and using raw will slow down the bursts or even limit their length.
4. You can mix 2) and 3), over-expose a bit and recover more from the raw.
5. You can of course shoot in manual mode, but you have to use your histogram regularly to check that your settings are still adequate.

Note that in all cases, since the bird is dark, your camera has less light to work with so this reduces the speed you can use. Since your camera AF will also struggle, you will have to use a small aperture to get some depth of field. Expect a large trash ratio.

Learn to shoot with both eyes open, one in the viewfinder and one outside. This makes birds a lot easier to frame.

(*) Unless you shoot seagulls, but these are easy targets, so you wouldn't be asking here...