How would I make it so that the order of something is randomized?

You can use math.random().

local children = model:GetChildren()

while wait(time) do -- put 'time' to how many seconds it takes to choose the next part
    local choosen = children[math.random(1,#children)] -- math.random() chooses a number from 1 to the number of children, which is 4 in your case
    local prevColor = choosen.BrickColor -- we store the previous color of the part
    choosen.BrickColor = BrickColor.new(newcolor) -- put newcolor to a color that the part changes to. if you want to put a random color, change this to BrickColor:random()
    wait(time) -- put 'time' to how many seconds it takes for part to return to the previous color
    choosen.BrickColor = prevColor
end