During an engine failure should I deploy 10° of flap or keep it clean?
You keep it clean: adding flaps adds drag. You can see this in Section 3 of the Cessna POH, which includes a Maximum Glide (distance) diagram. In the C172S POH that I checked, it notes that maximum distance is achieved with:


  
  SPEED 68 KIAS
  PROPELLER WINDMILLING
  FLAPS UP
  ZERO WIND
  


(A tailwind would extend your range, but only in one direction.)

Two other points worth noting:


If the engine failure also caused an electrical failure then you won't be able to use the flaps anyway (in models with electrically operated flaps)
You might want to reduce your gliding distance if the best landing spot is relatively close by, and extending flaps is one way to do that (along with slipping, S-turns or other maneuvers, and extending the gear)