Cleaner Left Linoleum Flooring Dull

I'm sorry this happened..something you could try is a floor wax to put a new finish on that would protect what finish is left. I would also stop using such a harsh cleaner. Ammonia is well known for removing the finish on flooring. A milder general purpose cleaner or even warm water with a little white vinegar is excellent for cleaning floors and is not so hard on them.