Does a tandem ultralight need flaps on the rear wing if the front wing has flaps?
As the love of tandems continues I will answer.  Because you are balancing lifting duties between two wings and (hopefully) still have the one in front stalling before the one in the rear, any configuration change in the front should be proportionately matched in the back so that the stall characteristics remain safe when flaps are deployed.

Deploying flaps increases the Angle of Attack of the wing and may cause a shift in the center of pressure.  So the design needs to be approached with care.

You could also put slats and flaps on both wings of a biplane too, but the whole point is to have one (smaller/less drag) wing for faster cruising flight and a larger, higher lifting wing for low speed flight (take off/landing).

For a GA personal use recreational aircraft, you may not need flaps at all.