Like you, I've never heard of anyone going from a federal circuit court of appeals to a federal district court, but that's not what he did.
The trick is that the courts in DC are federal courts, because the federal government runs the District, but they handle the matters that in the rest of the country are handled by the state courts. Judge Sullivan was on the District of Columbia Court of Appeals, which is not a federal circuit court of appeals. Per its Wikipedia article (my emphasis):
The District of Columbia Court of Appeals is the highest court of the District of Columbia. Established in 1970, it is equivalent to a state supreme court, except that its authority is derived from the United States Congress rather than from the inherent sovereignty of the states. The court is located in the former District of Columbia City Hall building at Judiciary Square. The D.C. Court of Appeals should not be confused with the District's federal appellate court, the United States Court of Appeals for the District of Columbia Circuit. The D.C. Court of Appeals and the Superior Court of the District of Columbia comprise the District's local court system.
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