If you want to glide the greatest distance, the last thing you want is to extend flap. Flap extension will always spoil the lift/drag ratio and therefore reduce the gliding distance from any particular height and IAS.
If you glide less distance from a given height, you will have an increased angle of descent.
If you fly down a steeper path at the same speed, you will lose more height in a given time- rate of descent increases.
So flap extension results in an increase in both angle and rate of descent.