Depending on your antenna and the size of the burgee, it may put excessive strain on the antenna. I am not a fan of mounting flags on antennas.
The typical mounting spot is the bow railing. There are various options available for mounting. Many Gradys have a hole in the most forward rail 'V' connector and that connector has a set screw. The standard available short flag masts fit that hole. A word of caution: If you use that hole with the set screw, it is strongly advised that you add a tether like a wire line clamped to the rail and the flag mast. The set screw mounts have a tendency to vibrate loose and the flag and mat can come loose and present a risk for personal harm and/or boat damage. In addition, it the mast comes loose and doesn't hit anything, it will probably fly over the windshield, out the back and into the sea. It has happened to me and others on this forum.
One other thing to think about is that although it may be too ugly weather wise to take the boat out, even at the dock or on land, the burgee will take a beating in stormy/windy weather. I have a sleeve with a tie chord that I use to reduce damage to the flag when the boat is docked. I roll the flag around the mast and slip the cover over it, tying the draw string around the rail. It looks like the sleeves you get with an umbrella. Your burgee/flag will last a lot longer when protected form the wind, rain and sun.