To protect the kettle, go to the store and get some large cotton balls. Stuff one or two of them in the spout and that should be enough to stop dust from getting in. This works best if the spout is the right size and you don't use the kettle frequently. If you do, it just means you have to be careful to keep the cotton ball clean. Just make sure not to set the cotton ball on a dusty or dirty surface like a counter and put it back in, you will be introducing dirt directly into the filter. If the cotton ball gets dirty, throw it out and use another one.
Alternatively, cardboard might work. You can cut out a piece of cardboard to fit snugly in the spout. Then take some string or fishing line and tape it to the underside of the cardboard. When you put the cardboard in, make sure the string is attached to the underside and the end hangs out of the spout. The cardboard will block dirt from getting in, and to take it out, just pull the string.