For a more elegant solution (without squiggles), use the dark red, dark purple, orange, green, and light purple flows as show above. Other flows as follows using X,Y grid with 1,1 at top left:
Light Red: Start at 1,11 (lower left corner), go up 4, right 2, up 4.
Yellow: Start at 2,6, go left 1 square, up 5, right 3, down 6, right 3, up 4, right 2, up 1.
LIght Blue (cyan): Start at 2,9, up 1, right 6, up 4, right 2, up 3, left 5, down 5.
Dark Blue: Start at 6,6, up 4, right 2.
For a more elegant solution (without squiggles), use the dark red, dark purple, orange, green, and light purple flows as show above. Other flows as follows using X,Y grid with 1,1 at top left:
Light Red: Start at 1,11 (lower left corner), go up 4, right 2, up 4.
Yellow: Start at 2,6, go left 1 square, up 5, right 3, down 6, right 3, up 4, right 2, up 1.
LIght Blue (cyan): Start at 2,9, up 1, right 6, up 4, right 2, up 3, left 5, down 5.
Dark Blue: Start at 6,6, up 4, right 2.