A US citizen can't be denied entry to the USA.

Remember, that plenty of people have dual citizenship, including dual US—other citizenship. Airline staff and immigration officers ought to be used to the concept, should it come up. Some might not be, of course, but as I say bear in mind that you are doing nothing illegal, or even unusual. That said, don't volunteer your dual status unless it is relevant, not because it is a problem but because officials often become confused when people do things that they are not expecting!