No. Radius of gyration depends upon the axis of rotation of the body.

For a solid cylinder, divide the radius of the flywheel by the square root of 2, to get the radius of gyration.

I believe it is I = mk^2 where k is radius of gyration and m is mass.

The radius of gyration is a measure, in mechanics, of the distribution of mass in an object relative to its centre of mass or a specified axis of rotation.

i thing radius of gyration does not depend upon mass because it is the distance between reference axis and the centre of gravity.