Latrell Mitchell torched the Dragons' right edge with four tries, vindicating Wayne Bennett's decision to keep him at left centre and leave fullback duties to the returning Matt Dufty, who starred against his old firm.
It was a case of deja vu for Flanagan at Accor Stadium on Saturday night as the Dragons were again competitive in patches, but not for long enough to prevent an 11th consecutive loss.
The Red V's latest defeat means they are winless entering their most important fixture of the regular season, the traditional Anzac Day clash with the Sydney Roosters.
Even with the Dragons four competition points behind second-last on the NRL ladder, Flanagan insisted he remained the right coach for the club.
"Of course," he said.
"(The Souths loss) puts pressure on me and puts the club under pressure.
"We're not winning footy games and I understand that. It's the business of winning and we're not winning.
"I go to work every day and all I can do is do my best, prepare the players the best I can. If it doesn't work and they've got to make a decision, I've got to live with that."
The Dragons were down 20-12 when Parramatta recruit Su'A flew out of the line to flatten Cameron Murray with a late and high shot in the 69th minute.
Referee Ziggy Przeklasa-Adamski consulted with the bunker before Su'A became the first player since round 22, 2024 to be banished from the field.
As the Rabbitohs marched up the pitch, Mitchell burst through the line for a third try of the night, before a fourth put the result well and truly beyond doubt.
Mitchell had earlier scored from a scrum play that embarrassed his opposite man Val Holmes, and nabbed a second try burrowing out of dummy half.
"I'm just really proud of him, Latrell," said Bennett.
"He likes to play fullback but we made a decision earlier in the season about his position in the centres and we had to make one change to that backline today, which was outstanding."
Saints were up against it after impressive hooker Jacob Liddle injured his hamstring in the warm-up.
"When things are going bad, they're going bad," Flanagan said.
In Liddle's absence, Damien Cook produced some vintage running form to help Saints hold a 12-10 lead until just before halftime.
But the Dragons were left to rue clocking off and allowing Alex Johnston to belt over down the shortside in the final 90 seconds of the first half.
It was the first of two tries Saints leaked while Souths were reduced to 12 men by Pete Mamouzelos' hip-drop tackle on David Fale.
Great white hope Dan Atkinson sprayed a kick out on the full in the red zone as the Dragons hunted second-half points down 16-12.
"We're just not getting it done. We can try hard. The NRL's not about trying hard. Evey team, every person in the competition tries hard," Flanagan said.
"You don't get points for trying hard."
Through it all, Dufty was magnificent in his first NRL game since leaving Canterbury midway through 2022 for the Super League.
Dufty, signed to a NSW Cup contract, ran for an NRL career-high 324 metres and fended off Kyle Flanagan to score down the right side in the second half.
