How would I calculate the mass of air in an empty flask?

From the volume of the flask, and the density of air under the conditions in the room, you can calculate the mass of air. The density of air varies with pressure, temperature, humidity, etc. At sea level and at 15 °C air has a density of approximately 0.001225 g/ml, so under these conditions, a liter flask would contain (1000 ml)(0.001225 g/ml) = 1.225 g of air.