The closest thing relevant might be Phenix City in 1954. According to Wikipedia, martial law was imposed to dismantle the local crime syndicate that was also in control of the local authorities. While elections were not re-run in Phenix (as Flynn suggests be done now), they were held under military supervision on that occasion:
Ahead of the 1954 elections for the Attorney General of Alabama, Phenix City resident and lawyer Albert Patterson ran a campaign for the Democratic Party nomination on a platform of ridding the city of crime.[6] Despite voting irregularities, he won the primary election, but was assassinated by shooting shortly afterwards on June 18, 1954, near his offices in Phenix City.[6] Patterson's murder caused unrest in Phenix City, with the Citizen's Betterment Association informing Governor Gordon Persons that the city was on the verge of anarchy. [...]
On July 22, 1954, after liaising with US President Dwight Eisenhower and FBI Director J. Edgar Hoover, Governor Persons proclaimed limited martial law in the city, allowing the national guard to take over law enforcement duties in Russell County.[18][6] It was reported that the national guard, armed with machine guns, shotguns and carbines, entered the sheriff's office and police department to disarm local law enforcement and confiscate their badges.[21] [Major General Walter J.] Hanna [Adjutant General of the Alabama National Guard] voided all weapons permits, and by July 23, the troops had confiscated 40 pistols and a submachine gun from the citizenry.[21]
[...]
Two weeks after the implementation of martial law, the mayor of Phenix City was jailed for neglecting his duties, and the city was administered by a group of military personnel chosen by Hanna.[18] In November 1954, when order in the city had been restored, the first free elections in decades were held, with armed guardsmen at each ballot box and supervising the count.[24] Having stabilized the situation, martial law was rescinded on 17 January 1955, and the city returned to civilian control.[25][26]
[...]
With the state Attorney General Si Garrett having checked himself into a mental hospital after being twice questioned over election fraud, the investigation into Patterson's murder and other major crimes in the city was carried out by acting Attorney General Bernard Sykes Jr. with a staff of civilian investigators and attorneys.[27][28][29] Under Sykes' direction, a grand jury issued more than 2,500 subpoenas and returned 759 indictments on more than 150 individuals, which was then a record for any grand jury in Alabama. All but two of those indicted were subsequently found guilty.[18]
Russell County's chief deputy sheriff, Albert Fuller; the Phenix City circuit solicitor (analogous to a district attorney), Walter Jones; and the state attorney general, Garrett, were all indicted for Patterson's murder.[26][28] Fuller was found guilty and sentenced for life; Jones was acquitted; and Garrett, who remained in hospital, was never brought to trial.[27][28] One of the key eyewitnesses to the murder was stabbed to death after testifying in open court.[30]
During his election campaign, Patterson had claimed it might take ten years to rid Phenix City of its lawlessness. His death and the subsequent imposition of martial law had meant it was accomplished in just seven months.[28] In 1974, the New York Times described the campaign as highly successful and stated that it had led to 20 years of relatively-low crime in Phenix City.[31] The incident was then the only instance of martial law being declared in a US city since the Reconstruction era that was not for reasons of civil unrest or natural disaster.[18]
