Buckwheat is more similar to a sunflower seed than grass cereal grains like wheat, but they have similar characteristics. Buckwheat has a hard outer shell (like wheat's chaff), with a starchy endosperm inside. It's the endosperm you need to grind into flour. I'm not certain, but I would guess the wheat you have already has its husk removed and is not the whole grain.
You can make flour from buckwheat by hand. However, using a motar and pestle to grind will be tedious labor, unfortunately. (But not impossible!) You need to pulverize the endosperm, which sounds easier than it actually is. If your buckwheat is whole grain, you will need to first remove as much of the germ as possible.
I'd suggest using an electric grain mill if you're intensely about serious turning it into flour. A decent grain mill costs $175 or more.
Personally, I'd make use of the buckwheat as an additive or topping for other breads I make. A flatbread with millet and buckwheat flour (purchased or milled yourself) would be good.
Lastly, if you have no immediate use for the buckwheat: It'll keep for about 2-3 months in a sealed container in the fridge or 6 months or longer in the freezer.