The only two times the Flyers opened the postseason with a best-of-seven series sweep were in 1974 and 1975. And if you aren't sure why that is significant, you're reading the wrong blog. And keep in mind, that each of those sweeps was completed with an overtime victory.
Also, since the NHL went to four full best-of-seven rounds (1987), 19 of the 24 Stanley Cup champions (79%) had at least one 4-0 sweep along the way. That percentage even holds true back through to the 1968 expansion (34 of 43).
Here are the Flyers' 4-0 sweeps: