Are there any game mechanics that affect gem drop quality?

Does having greater magic find or gold find affect the quality of the gems dropped? If I have a decent amount of magic find and a monster was going to drop a Chipped Ruby, is it possible for the magic find to update it to a Flawed? Or it is based solely on the difficulty level you are on and the static drop rates of gems?

Solution 1:

Gems are not magic items (their names are in white, not blue/gold/green), so increased chance to find magic items does not affect them.

In Diablo 2, increased MF did not affect gem drops, and I haven't heard anything about this changing in D3.

Solution 2:

No.

As you can see in What does increased magic find do? and the recap

Magic Find has always been one of the most popular item attributes in Diablo. Magic find helps increase the probability that a higher quality item will drop from monsters.

Conclusion

This need more tests, but you can follow the main idea. Magic find does not increase the drop chance for gems.