Upvote:3
Looking at the applicable regulations, 8 CFR ยง 217.5 says that
"Each nonimmigrant alien intending to travel by air or sea to the United States under the Visa Waiver Program (VWP) must, within the time specified in paragraph (b) of this section, receive a travel authorization" (emphasis mine)
This specifies that non-US citizens must get an ESTA, but doesn't specify anything about US citizens. When applying for an ESTA you are required to list all other nationalities. The form will allow you to enter US citizenship as an additional citizenship.
It's hard to find information about whether people have been successful with their ESTA applications when disclosing that they are US citizens. The only way to find out may be to file an application.