2751 (2014), in which he successfully led litigation challenging the Affordable Care Act's contraceptive mandate on behalf of Hobby Lobby stores.

[1] On September 28, 2017, President Donald Trump announced his intent to nominate Duncan to an undetermined seat on the United States Court of Appeals for the Fifth Circuit.

[1] On October 2, 2017, he was officially nominated to the seat vacated by Judge W. Eugene Davis, who assumed senior status on December 31, 2016.

v. Gloucester County School Board in a suit brought by a transgender student, Gavin Grimm, over bathroom access.

Duncan noted, "Congress has said nothing to prohibit courts from referring to litigants according to their biological sex, rather than according to their subjective gender identity".

[22][23] On March 9, 2023, Duncan arrived to Stanford Law School in order to participate in a discussion on "Guns, Covid and Twitter," having been invited by the university's Federalist Society chapter.

The event became a cause célèbre, and was marked by protests led by the student coalition Identity and Rights Affirmers for Trans Equality (IRATE) after a request for his speech to be canceled was denied.

[24] According to The Stanford Daily, "Throughout Duncan’s speech, student protesters booed and made various loud comments, frequently drowning out his voice.

In fliers put up in advance of the event, protesters called Duncan a right-wing advocate for laws that would harm women, immigrants and LGBTQ+ people."

19-20565, denying the fourth habeas corpus petition and a delay of execution for Larry Swearingen, who was convicted of the 1998 murder of Melissa Trotter.

The court noted that these "'new' claims in this latest phase could not possibly have made any difference to the outcome of his trial" and have "not come close to establishing that 'no reasonable fact-finder' would have found him guilty.

[40] This opinion has received scholarly attention as an example of common-good constitutionalism, a socially conservative judicial philosophy recently proposed by Harvard Law professor Adrian Vermeule.

[41] Duncan was on the three-judge panel which halted the Biden Administration's OSHA rules mandating COVID-19 vaccinations or weekly COVID testing in the workplaces with 100 employees or more.