I've no idea if there is a proper order but I do:
back (least likely to have tangles) with pinned brush,
followed by ears - Spaniel so takes ages and needs doing on top/outside and underneath (usually do outside first, underneath, then back to outside to finish) on each side (plus I do each with a pinned brush, followed by a gentle slicker brush)
Next I get the special triangle shaped slicker to make sure the small grove behind where his ear and head meet is tangle free on each side.
Chest with pinned brush and gentle slicker.
Legs (again Spaniel fur makes them trickier) - first I tease out knots/tangles where all the little mini leaves and twigs and mud have got with my fingers, then i do the long bits with pin brush, then gentle slicker.
Then I do his long furry tummy. Then he needs between his back legs and his manhood carefully brushing (prone to nasty tangles there if I don't) - again I use pin brush, then gentle slicker.
Then tail with pin brush.
Then soft brush on his head
Then gentle slicker on his back and lots of treats.
Basically I start and end with the area he is happiest to have done.