You can mix instant coffee with water, milk, cream, or any mixture of those, to your taste. It doesn't matter, and you don't have to do it in multiple steps.
This is different from fresh ground coffee. In ground coffee, you are making an extraction, which is a complicated chemical process. Your solvent has to get behind cell walls and get out again, this time with the solute in it. You never get full extraction anyway. Many factors such as heat, other stuff dissolved or dispersed in the solvent, etc. can hinder this already problematic process and give you a much weaker or different-tasting result.
Instant coffee is specifically made to be 100% soluble in water, so you only have a solution happening, not extraction. The process happens to be not very dependent on temperature (this is different for all combinations of solvent and solute). Maybe it is a bit slower in cold water, but the difference is not really noticeable in practice. The fat content in milk or cream is also not high enough to disturb the solution. So you can just do it any old way you want and you'll end up with 100% dissolved coffee.