I haven't played my flute in several years, but it is a fairly high-quality open-holed silver instrument. During this time, it is already a bit tarnished and grimy, and I want to make sure that I am not further damaging any of the instrument by the way that I am keeping it stored currently. What's the best way to store a silver instrument so that the pads, silver, and sound maintains its integrity?
For the silver there is no problem. You'll have more work to get it shiny and can reduce the amount of work needed before putting it into use again, by using a silver cleaning cloth from time to time. Liquid agents are difficult to apply, so that the pads don't get in contact. For the pads, unfortunately, there is not much you can do beside avoiding damp or overly dry environments. They simply become harder over the time. After several years of storage (and some time of use before) I assume, they already need to be replaced, so situation won't become worse here either.
You can clean the silver with a silver polish cloth. Use these sticks to clean your ears for the hard to reach places.
It's also important to keep your mechanics going smoothly. So buy a small bottle of special flute oil and put a little on the joints (hinges?).
Use a cloth on a stick to dry out the inside of the flute after each time you play it.
When you notice the keys start making noise or not keeping the air in, it is time to get your pads replaced.