Stiffness is defined by the ratio of Force applied to change in dimension. you could probably form a film and conduct a film testing of the filler. Shear Testing can also be used to quantify stiffness. 

when you say filler stiffness, is it with repsect to filler an a bulk material or filler as a part of composite and the stiffness enhancement it impart?

from what i understand, to calculate stiffness you can do either the tensile (more material required) or compression test and the modulus is calculated from its stress-strain response ( force vs displacement curve)

But if you want to know the range of stiffness value you composite might impart then you do the same for pure materials.

Maybe if you give a bit more detailed description of the problem with regards to stiffness then it might be more helpful for us.

Stress - strain behavior provides Modulus not stiffness. Modulus involves the geometrical factors too. 

for polymers, there are substantial relationship between modulus and stiffness. For ex: for axial stiffness: K : AE/L where K is stiffness and E is elastic modulus. I do understand E is in intrinsic property and K depends upon on the microstructre but it equally for important to understand what does Norjulia Ahmad Mahir what to know so as to provide a much more scientific answer

Calculation of force / displacement also includes geometry since there are specific standard one need to follow for stiffness test i.e 3/4 point bending

Perhaps you can use the suggestion of Nischith Raphael and do some nanoindentation experiment on thin films or if you even have the possibility to seperate the filler completely from the matrix material, you can probably also do some nanoindentation test directly for the filler.

A problem with nanoindentation or AFM measurements might be that the result depends on the structure of your filler. If you have a single particle it is easy but as fillers are typically small and have active surfaces they tend to agglomerate and what you will measure is the stiffness of these agglomerates.

On the other hand depending on your mixing process you will also find different portions of agglomerated respectively seperated fillers in your rubber mixture. Therefore the results could be important or not.