Grey (black) and Fox squirrels, limit of 5, possession of 15. Reds are considered furbearers and aren't supposed to be shot. You need a trappers licence.
Interesting, squirrels fall under schedule C animals, here’s what is in the bc regs for schedule B & C:
Schedule B and C wildlife are known to destroy property and/or are detrimental to native wildlife or habitat. These species have fewer restrictions regulating their hunting, killing or capturing. Any capture or killing
of these species must still abide by provincial laws regarding the humane treatment of animals.
» Schedule B lists animals that may be captured or killed on private land only for the specific purpose of protecting property; no hunting license or open season is required. On Crown land a person must abide by the open seasons for Schedule B species (see Regional Schedules for open seasons). Schedule B species include coast mole, snowshoe hare, lemmings, bushy-tailed woodrat, deer mice, porcupine, northern pocket gopher, yellow-bellied marmot, woodchuck, Columbian ground squirrel, striped skunk, raccoon, and spotted skunk.
» For all Schedule C species there are no closed seasons or bag limits. Furthermore, there are no requirements to remove edible portions or report the killing to an officer. Schedule C birds may be hunted using electronic calls.
» You do not need a hunting licence to capture,
hunt or kill the following Schedule C wildlife: American bullfrog, green frog, snapping turtles, North American opossum, eastern cottontail, European rabbit, nutria, gray squirrels, fox squirrels, house sparrow, European starling, and rock dove (domestic pigeon).
» You do need a hunting licence to hunt the following Schedule C wildlife UNLESS you are hunting them on your property or they are damaging your property: Feral Pig, Northwestern Crow, American Crow, black-billed magpie, and brown-headed cowbird.