Air has no chemical formula because it is made up of a whole bunch of stuff. It's a mixture. It would be like asking: what's the chemical formula of orange juice? Mixtures like orange juice or air don't have formulas. Orange juice is made up of water, sugar, citric acid, and small amounts of other stuff. Water, sugar and citric acid have chemical formulas, but the juice itself does not.

Similarly, air is like juice, but it's a mixture of gasses. It is made of mostly nitrogen and oxygen with a bunch of other stuff in small amounts. Here's the breakdown with their chemical formulas. By volume, air is about:
78.084% Nitrogen (N2)
20.947% Oxygen (O2)
0.934% Argon (Ar)
0.033% Carbon Dioxide (CO2)

With trace amounts of:
Neon (Ne)
Helium (He)
Krypton (Kr)
Sulfur dioxide (SO2)
Methane (CH4)
Hydrogen (H2)
Nitrous Oxide (N2O)
Xenon (Xe)
Ozone (O3)
Nitrogen dioxide (NO2)
Iodine (I2)
Carbon monoxide (CO)
Ammonia (NH3)
Water (H2O)