Kadri, who signed a new two-year deal on the eve of training camp, is expected to produce, while Raymond is with the Leafs on a tryout basis after 374 games with the Vancouver Canucks.
Performing in his hometown, it was Kadri opening the offence as the Leafs scored three in 3:05 for an early 3-0 advantage.
Kadri, who also starred in the Budweiser Gardens for the Ontario Hockey League's London Knights, began a two-on-one rush inside his own blue-line. Kadri used a drag move to awkwardly put Philadelphia defenceman Hal Gill out of position before snapping the puck past Steve Mason.
Troy Bodie, who split his AHL time between Portland and Norfolk last year and was inked as a free agent by Toronto in July, made it 2-0 by beating Mason in close. Bodie received his pass on the doorstep from 2013 first-round pick Frederik Gauthier.
The third Toronto goal displayed the speed of Raymond as he scored short-handed on a breakaway after stealing the puck at his own blue-line and out-raced Philadelphia's Erik Gustafsson down the right wing.
The Cousins goal was started by a Gill point shot that went wide of Leafs goaltender James Reimer's net and bounded out the other side for Cousins to flip in a backhand.
The final period was scoreless.
In 28 minutes of work, Reimer stopped 14 of 17, while counterpart Mason stopped 12 of 15. Maple Leafs' Christopher Gibson didn't allow a goal in 32 minutes and was credited with 13 saves, while the Flyers' Anthony Stolarz was beaten in his first minute, but settled down to make 14 saves on 15 shots.
The two clubs meet again on Monday at Air Canada Centre in Toronto. The Leafs tune-up schedule includes eight games over 14 days before opening the campaign Oct. 1 in Montreal.
The Flyers open their regular season versus Toronto at home Oct. 2.