You can consider dripping a drop of water (if it is ok to do so) to compare the contact angle (http://soft-matter.seas.harvard.edu/index.php/Contact_angle).

hBN < 90° (Article Liquids with Lower Wettability Can Exhibit Higher Friction o...

Graphite ≥ 90° (Article What Is the Contact Angle of Water on Graphene?

the exfoliated flakes are only tens of micrometers across. So the I really don't see how this can be feasible for me.

Dear Gokul Krishna , unless you have some extra information from your lab-mate, such as wafer labels or other kind of identifications (such as scratches, chipped borders, etc), some indication about the number of layers in each type of flake (like monolayer graphene, multilayer hBN), it would not possible to distinguish between them by optical microscopy given they show a high transparency and low contrast. Even using polarizers would not solve the problem.

I think the simplest and fastest way to know what wafer belongs to graphene or hBN is by means of Raman, it will take just a few seconds, the time to focus on a flake and getting the spectrum. Actually you only would need to analyze one wafer, if the spectrum show -say- graphene, the other wafer would be hBN (and vice versa.

Hope this helps. Good luck with your research and best wishes.

Alternatively you could also test the conductivity of one flake, using needle contacts, and if it is conductive it would be graphene and if not it would be h-BN.

Still, the Raman option is the fastest.

Regards!