Does a tandem ultralight need flaps on the rear wing if the front wing has flaps? Does a tandem ultralight need flaps on the rear wing if the front wing has flaps?

I understand that most Rutan canards don't have flaps as I was told if the main wing has flaps, the canards need one too.

Rutan did make one with flaps on both the canard and the main wing.  I think it was called the Grizzly.

So... what about a tandem aircraft (with positive lift on the horizontal tail) with flaps on the front wing ? Does the rear wing need flaps too?

Can't you just use the horizontal trim tab as a flap if you need more rear lift to offset extra lift of the main wing with flaps extended?  

After all, wouldn't most conventional aircraft with rear cg and slow flight ( low Cm) in a dive with a symmetrical horizontal tail, with elevator down, be generating positive tail lift anyways, so they are acting like a tandem aircraft, no?
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.