Flaherty is the nephew of Cowboys coach Jason Garrett and tight ends coach John Garrett. Another uncle, Judd Garrett, is the director of pro scouting. His namesake father played two games for the Cowboys in 1987, and also spent time with the Eagles and in the USFL.
The younger Flaherty, a Princeton product, went to camp with the Saints last year, and worked out for the Cowboys in December, and New England recently.
“It’s pretty interesting,” Flaherty said. “This is my first day here, so it’s definitely going to be an interesting experience, but I’ve been around their coaching a lot through the years.”
Nagy suffered a high ankle sprain, and is seeing a specialist this week. If he clears waivers, he’ll revert to injured reserve.