Should plumber's putty be placed on the sink or on the flange during a flange install?
There is no "right way", but the "theory" is: 

On a loose fitting (fitting has play inside the hole), placing the putty on the sink will create a better seal on the area actually making contact. On a tighter fitting, placing the putty on the flange will seal the areas closer to the center leaving less room for voids. See this diagram (tight fitting on top, loose fitting on bottom, "risk" for voids/incomplete seal in red):



Honestly, while the "theory" isn't bad, in practice it simply requires that you use enough putty to make a good seal. The net effect is that the putty just needs to be sandwiched between the flange and the sink to prevent water from leaking, either from an (intentionally) stopped sink into the overflow (bathroom) and thus down the drain, or from around the flange into the cabinet below when the flange acts as a reducer or on sinks without overflows (kitchen).

So, whichever way works best for you is the "right way".

Edit: Updated diagram to reflect the proper amount of putty.
Edit(2): Updated diagram to reflect proper amount of putty including over-puttying.