How can I add a sound to all my speakers?

The best way to fix this is by using coroutines

Coroutines create a separate thread where you can run your loops without disturbing the flow of your main script.

There are 2 key functions that you require:

coroutine.resume(c) - c being a created coroutine

coroutine.create(f) - f being a function

You must create a coroutine before using it (by calling resume()) There are a couple of ways of making a coroutine, I will show you one.

coroutine.resume(coroutine.create(function() 
 -- Your either looped script or for script
end))

So, for you it should go like this:

function AddSounds(Object, Sound)
    if Object:IsA("Part") then
        if Object.Name == "Speaker" then
	    coroutine.resume(coroutine.create(function() 
            	local S = Sound:Clone()
            	S.Parent = Object
          	WaitTime = S.TimeLength
          	S:Play()
           	wait(WaitTime)
         	S:Destroy()
          	SoundAdded = false
           	print("Ready to play")
            end))
        end
    end
    for _, child in ipairs(Object:GetChildren()) do
        AddSounds(child, Sound)
    end
end

By the way, your print("Ready to play") will print once the play has finished, which I do not believe you want. Add it before S:Play()

Hopefully that should work for you.