How to add a cooldown to this NPC chat?

For this, you're going to want to use a debounce as theking48989987 commented on your post. To do this you just need a simple true or false statement

local debounce = false -- Saying it's not being used
function onClick(click)
	if debounce == false then debounce = true -- Checking if it's not being used, and if it's not, setting it to being used!
		for i,v in pairs (script.Parent:GetChildren()) do
		    if v.ClassName == "ScreenGui" then
			    c = v:Clone()
			    c.Parent = click.PlayerGui
		    end
		end
		wait(3) -- waiting 3 seconds
		debounce = false -- Setting it back to not being used, therefor it can be used again
	end
end
script.Parent.ClickDetector.MouseClick:connect(onClick)