How do you find the density of a metal?

The data from your experiment is insufficient to determine the density of the metal.

Density of the metal = (Mass of the metal) / (Volume of the metal)

Mass of metal can be easily found by the difference in mass before and after the addition of the metal.
Mass of metal = (103.25 - 82.56) g = 20.69 g ≠ 23.94 g (as you quoted)
This comes a contradiction among your data.

If you used a graduated cylinder, the volume of the metal is equal to volume of water displaced by the metal. But now, you have used a flask instead, and such instrument could not be used to find the volume of water displaced by the metal. In other words, the volume of the metal is unknown, and thus the density of the metal CANNOT be found.

If you weighed the flask with the stopper before addition of water, you could find the mass of water.
Volume of water used = (Mass of water used) / (0.9966 g/cm³)
However, this is the volume of water used in your experiment, but NOT the volume of water displaced by the metal.

You need to be able to measure both the exact change in mass AND the exact change on volume.

The density of the metal is: (change in volume) / (change in mass)

Without both, no calculation is possible.