The problem is the usual one which is that they operate about ten times faster than us humans. The only feasible way to photograph them in flight is to catch them in the split second after taking off.
I was experimenting with shutter speeds in this session and discovering that 1/1000s is too slow. My usual 1/4000s would have been more appropriate although light levels were low which pushed up ISO settings.
I used the Canon EOS R5 with the RF 24-240mm STM lens. This lens is not the most brilliant optically but it focusses super fast and works well for birds in close.