Does milk make eggs more fluffy?
While adding milk may change the flavor slightly, such a small amount is used that it is not likely to be an extreme loss of flavor.
Some people add a small amount of water. With a small amount, flavor loss should not be noticeable. And since most people scramble their eggs with butter or some other type of oil, there is a measure of fat included. (Ref. to below quote.)
 Yahoo Food  explains the effect and differences:

Some recipes for scrambled eggs call for water or milk. Does this do anything for the eggs?
When eggs are scrambled, the mechanism that transforms the liquidy beaten eggs into a fluffy mound on the plate is protein coagulation—the process by which, when exposed to heat, proteins unfold and then tangle up with one another and set, forming a latticed gel. The more tender the scrambled eggs, the more loosely the proteins have coagulated. Adding water to scrambled eggs dilutes the proteins a little, thereby raising the temperature at which they coagulate and making it harder to overcook the scramble. Water also increases the amount of steam, which puffs up the eggs, producing fluffy scrambled eggs. As for milk, it contains water but also fat, which coats the protein molecules so that they can’t bind with one another as tightly. The key to scrambled eggs that are both fluffy and tender is a balance of water and fat.

Also you can choose not to add anything and just whisk the eggs very well before cooking. This will incorporate air and result in fluffier eggs.
In the end, it will be your choice. I would suggest trying all three ways and deciding which you like best.