Never? That's a real 'wow' if so.
Here is the
official word based on zero PIMs by Flyers' opponents
The game marked just the eighth time in Flyers history that their opponent did not commit a single penalty. The list:
Vegas Golden Knights 2018/02/11 @VGS
Ottawa Senators 2006/11/22 @ PHI
Ottawa Senators 2002/01/22 @ PHI
Los Angeles Kings 1978/04/01 vs PHI
Minnesota North Stars 1976/12/14 vs PHI
Minnesota North Stars 1976/12/01 vs PHI
Montréal Canadiens 1972/02/19 vs PHI
Los Angeles Kings 1967/12/08 vs PHI
From what I can tell, the prior fewest PIMs combined was 2 in the December 8, 1967 game. However, the NHL box score lists Joe Watson with two holding penalties at the same time which could be an error since such wire service entries weren't as detailed as today (two holding penalties on the same play seems beyond unusual).
If the previous low wasn't 2, the other games in which 4 PIMs was the low occurred in games played on December 1, 1976 (Minnesota North Stars) and January 22, 2002 (Ottawa).... and maybe, but I doubt it, that 1967 game against Los Angeles.
From what I see (unofficially), there have been three games in which the Flyers recorded zero PIMs:
at St. Louis in 1979 (Blues 2 PIMs)
vs. Phoenix in 2000 (Coyotes 10 PIMs)
vs. NY Rangers in 2011 (Rangers 6 PIMs)
To clarify all this minutia:
2 PIMs in a game involving the Flyers has happened either two or three times:
at Vegas Golden Knights, February 11, 2018 (Flyers 2, Vegas 0)
vs. St. Louis Blues, March 18, 1979 (Flyers 0, St. Louis 2)
(probably) vs. Los Angeles Kings, December 8, 1967 (Flyers 2, Los Angeles 0)
So, yes, based on my previous comment there has never been a game in which the Flyers and opponent played penalty-free.
(edited to hopefully avoid confusion).