How to get global variables to work outside of a function?

Simply put the local variable before the block like this

local button = script.Parent
local otherdoorbutton = script.Parent.Parent.DoorR
local db = false

button.MouseButton1Click:Connect(function()
	local train = workspace[tostring(game.Players.LocalPlayer) .."Train"]
	local dooropened = train.DoorOpened

	local track -- before loop it is still in this scope so all good	
	
	for i = 1,6,1 do
		local door = train["DoorL" ..tostring(i)]
		local anim = door.OpenClose
		local controller = door.AnimationController

		--/changes the track variable from outer scope
		track = controller:LoadAnimation(anim)

		if db == false then
			if  dooropened.Value =="NO" then
				track:Play()
			end
		end
	end
	wait(3.5)
	track:AdjustSpeed(0) --this does work
end)

The thing when you said gives you 'error' when you remove local is not an error but warning, i am glad you counted this as an error as it prevented you from doing the stupid thing like that, assigning global variable like this without local will allow the whole script to have access to it, no matter in what scope you are, this is generally bad because your script is not supposed to have access to it.

Also using not keyword is a lot better than == false because it's a lot better to type and faster too.

if not db then
	...