How did the philosophy of "Gospel of Wealth" develop into an American attitude of superiority?
The Gospel of Wealth held that men (at that time) who became rich should use their wealth for the benefit of society as a whole. You can argue that this idea combined with Social Darwinism to help create the idea that the US should go out and conquer and civilize other peoples.
These two ideas, when combined, argue that the people who have the most wealth are superior and should use their superior abilities to help the inferior. This was the sort of attitude that led to US imperialism and to the general idea of the "white man's burden." In this way, you can argue that the Gospel of Wealth helped create the attitude that the US was superior to other countries.