Flying eggshells

What is probably being referred to here indirectly is the fact that air with moisture in it is less dense that dry air. The question becomes, is the buoyancy force of an empty egg with the optimal moisture content of air sufficient to overcome it's weight?

Searching around I see that water vapor has a density of 0.804g/Land dry air has a density of 1.27 g/L. So from that I will revise my interpretation of the question.

Will an empty eggshell full of water vapor rise at STP?

Volume of an egg = 52 ml, therefore weigh differential is (1.27-0.804)*0.052 = 0.0242 grams.

With an egg shell typically taking up 11% of the weight of an egg (being 50 grams), and 11% is 5.5 grams.

TLDR: No

No. For the same reason that you can't pick yourself up by your shoelaces. However, if you were to fill a container with water and close off the escaping steam with the eggshell, it would be possible to "levitate" the eggshell with the rising steam.