May I grease and flour a glass baking pan instead of using parchment paper?

You should be fine with greasing and flouring your pan. Obviously you won’t be able to remove the cake before cutting it, but no big deal. However, glass conducts heat differently than metal, and the outside of the cake will be done before the center. You might want to lower the temperature, bake longer, and test often near the end. Sounds like a delicious cake — good luck.