Flores filed a lawsuit Tuesday against the NFL, the New York Giants, Miami Dolphins and the Denver Broncos. Rivera said it was a situation he wanted to look into more to better understand, but he said he also knew that Flores warranted another job offer because of his background. Miami fired him last month after three seasons, including winning records in the last two.
"He's very impressive and we had a great interview," Saints general manager Mickey Loomis said Wednesday from the Senior Bowl in Mobile, Alabama.
Rivera spoke for nine minutes on the topic during a video conference call designed to discuss Washington's new name.
"This is a very accomplished coach," said Rivera, one of three head coaches of color in the NFL. "I can see the frustration and I can feel the frustration. It's almost as if this is your last resort. How does a guy like that get left out of the hiring cycle?
"If you put his résumé -- and took the name off and changed the team he coached for and grew up with -- and put it on the table and looked at all the résumés, Brian Flores is the type of résumé you point at. Let's judge on merit."
Rivera also said other Black coaches such as Leslie Frazier and Eric Bieniemy should be hired.
Frazier, currently the Buffalo Bills' assistant head coach and defensive coordinator, was a head coach with the Minnesota Vikings from 2011 to '13; Bieniemy, the Kansas City Chiefs' offensive coordinator and a former NFL running back, has never been a head coach.
"Leslie Frazier is the type of résumé you point at. Eric Bieniemy is the type of résumé you point at. Why? Because the merit," Rivera said. "These guys deserve opportunities. They deserve a chance, and to me that's what the Rooney Rule stood for. It's a chance to open the door and get your foot in and then merit speak for itself. That's the issue here."
Rivera said it wasn't until his eighth interview that a franchise -- the Carolina Panthers in 2011 -- hired him to be a head coach.
Rivera, who once was a part of the NFL's diversity committee, said he's heard the frustration from other assistant coaches. He recalled an informal dinner where former NFL commissioner Paul Tagliabue spoke to minority coaches, all of whom were coordinators at the time. Each one had a chance to speak their piece, Rivera said. Several owners, including the Pittsburgh Steelers' Dan Rooney and Dallas Cowboys' Jerry Jones, also attended and spoke.
"I remember listening to the frustration of some of these guys talking about not getting the opportunities," he said.
Rivera said he liked what Troy Vincent, the NFL's executive vice president of football operations, has done in conjunction with commissioner Roger Goodell.
"The league has done good things and probably can do more," Rivera said. "The key is to find opportunities and avenues and put these guys in front of the people that make decisions. If you do this you have to hire people of merit off what they accomplished."
ESPN's Mike Triplett contributed to this report.