You don't need grass seed becuase planting grass will mean watering that grass which will eventually kill the oak tree.
Oaks don't take to underplanting or supplemental watering. It will cause rot and kill the tree.
You could add a few half wine barrels or whiskey barrels full of spring and summer bulbs and that would not pose a problem. Planting them with seasonal annuals for color is fine too.
Planting anything in the ground disturbs the oak's roots and increases the watering in the area. That's harmful to the tre.