WWII air raid sirens were built just like drilled disk brakes -- the noise is designed in to them. As the holes In the disk go around and between the pads the trapped air expands and makes a little noise as it is then 'freed' by exiting the pad area. This noise is not uncommon, but not everyone hears it.*
Chamfering the holes might change the tuning of the 'note', but unless you can stop the trapped air from expanding (braking heat) as it goes through the pads they'll continue to make noise. In other words, it would be a great exercise is countersinking stainless plate, but you'll change your tune when it's over. IMO, your best bet, if it bothers you, is to either use non-drilled disks or try changing your pad compound and design. Pads with grooves cut in the surface let air escape and reduce the tendency to sing.
My left front sounds like a buzzing bee with its balls in a vise, but only on hard braking, and I hear it only below about 15mph. A buddy of mine has his somehow 'tuned' to what sounds like a perfect 5th. He swears he didn't plan it that way. When I hear them from behind it sounds like a tiny locomotive sneaking up on me.
*based on conversations with brake people. This is all anecdotal, with no real experiments to back it up. Sounded reasonable to me though.
