How to make all parts within a model change color in sync?

Here you go, with some extra indirection and parametrisation thrown in:

local model = script.Parent
local delta = 1.1 -- time between colour changes

--list of colors to cycle through
local colors = {
			Color3.new(0,204,255), 
			Color3.new(0,255,0),
			Color3.new(255,255,0),
			Color3.new(255,0,0),
			Color3.new(153,0,153), --EDIT: missing comma
			Color3.new(0,0,255)
		      }

-- infinite loop
while true do
	--loop through each of the colors
	for _, c in pairs(colors) do
		--for each color, set all of the parts in the model to that color
		for _,p in pairs(model:GetChildren()) do
			--make sure this child is a part
			if p:IsA("BasePart") then
				p.BrickColor = BrickColor.new(c)
			end
		end
		wait(delta) --wait 'delta' seconds before next color
	end
end 

Insert into the model whose parts you want to change color. Edit the list of colors or the time delta to tweak the animation and cycling through the colors.