In the attic of my upstairs of my home I have 15.5" of blown in insulation.  There's a work order in my attic (from the previous homeowners) stating the 15.5 inches of insulation is equivalent to R36.  

Anyway, i'd like to install some flooring in the attic so I can utilize the space for storage.  To be able to do this i'm obviously going to have to pack some of this insulation down to be able to lay flooring on top of the rafters.  Will this diminish the R-value of the insulation if I pack it down?

Dont pack insulation - it will reduce R value.  Remove what is needed to lay down your flooring.... and deal with the fact that you have worse insulation R value wherever you floor over.

If you absolutly must have a floor up there. You best bet is to take out the insulation until you have just enough left you can floor over without packing any down. Yes you will lose your R value.