Let us see the basics: there are certain flaws in the conventional flywheels that are not really well-designed.
At any given rotational velocity, the linear velocity near the edge (periphery) will be higher. Air coming in contact with the peripheral regions will be thrown out in a direction perpendicular to the rotation axis. This flow will take away the energy from the flywheel but cannot be avoided.
Like a centrifugal fan, the pressure will be higher near the periphery and air will be sucked in from the central region.
Spoked designs are popular because of mechanical considerations; the stress produced by the centrifugal force is not uniform and can cause failure. Modern idea is to have lighter mass and higher rotational velocity; because the energy stored is proportional to the square of the angular velocity, higher speed produces greater energy storage (that is the principal job of a flywheel).
To reduce stress, it is better to have a number of light disks stacked together; the centre one will be the largest and the outer one will be smaller in size; they can be stuck together with glue (and the edges nicely bevelled). You will end up with a flywheel that is fat at the centre but thinning out near the edges.
The airflow will still be there but the flow will not be turbulent and less energy will be lost due to friction with the air. In short, no spokes!
My suggestion: fill up the flywheel with foam (no stress for all practical purposes) and then cover the surface with a smooth foil. You may be able to reduce the loss by half!