>>11175278No. For a fly to, well, fly, it must supply a downward force to the air equal to its weight. In a closed container, that air cannot escape, so its motion supplies a downward force to the container that is exactly the same as the weight of the fly.
Now, the apparent weight of the jar will fluctuate slightly as the flies accelerate and decelerate, but the fluctuations will always average out to the weight of the flies.
Also, if the container isn't sealed, such as an open cage, then the air can escape into the environment without transferring its full downward force to the cage, and it will be lighter when the flies are flying.