To a degree you will always be dealing with some 'unknowns' shooting wild birds in flight. Which makes me conclude that there is certainly no 'best' technique that fits all situations.
You Will be making trade-offs , the sum of which should be that you're satisfied with the degree of wing blur , ISO noise , depth of field , price of gear , and so forth.
That being said, one should understand that auto iso is aiming at a goal of appx 18 % gray for a portion of the image or overall.
If your bird is not of that brightness ,, for ex a crow is nearly black,, then a brightness of 18% gray is actually inappropriate for a target crow.
It is NOT an ideal exposure to satisfy auto ISO standards. Your camera will indeed expose a gray card well with auto iso , you just dont want to look at images of gray cards
Depending on your camera gear , the very bright light you may end up with (as background trying to expose the subject to 18% gray brightness),
tends to overwhelm the pixels and sky starts overflow into adjacent pixels ,,
try doing this intentionally and extremely , You'll see the sky begins to soften the edges of the crow.
To combat this loss of detail , a result of too much light, you might aim to underexpose a bit , and in post processing, lighten up the dark areas instead of trying to darken the sky.
If you do take this angle, do not rely on 'lighten shadows' sliders heavily, because this
magnifies the look of graininess in the dark areas.
What you Do do is lighten the 'blacks' slider
and simultaneously Darken! the shadows,, (just not as much as you lighten the blacks)
your dark areas will be much smoother and you will end up with much less or no halo of lightness around the perimeter of the bird.
Taking this approach , you can have marginally faster shutter speed ,and better detail , and not blow out the sky making it look like white paper.
If you Do end up lightening the blacks considerably , you will see a drop in the color contrast, and this is countered by a small increase in vibrance ( not saturation) .