"Play is not a valid member of Animation "Workspace.snipperdiaper.Tool.Animation"?

The error tells you exactly what the problem is: Animation objects do not possess a method called "Play". AnimationTracks possess this method and they can only be obtained by using the LoadAnimation of a humanoid's animator. You've already used it (not on the Animator though, Humanoid:LoadAnimation) is deprecated) but you used the Play method on the animation itself instead of the created AnimationTrack.

Here's what it should be, and I've also adjusted other parts of the code that could've been simplified:

• Use variables to help shorten your code
• Instead of writing multiple lines to change the text and yield the thread, use a for loop instead
• You can use the Activated event which fires when the player clicks their left mouse button while the tool is equipped instead of using an event that fires every time it's clicked and check if the tool is equipped

local Animation = script.Parent:WaitForChild("Animation")
local tool = script.Parent
local player = game:GetService("Players").LocalPlayer
local char = player.Character or player.CharacterAdded:Wait()
local hrp =  char:WaitForChild("HumanoidRootPart")
local humanoid = char:WaitForChild("Humanoid")
local debounce = true
local mouse = player:GetMouse()

local AnimationTrack = Humanoid.Animator:LoadAnimation(Animation)
local teleport_gui = player:WaitForChild("PlayerGui"):WaitForChild("ClickToTeleportGui")
local teleport_label = teleport_gui:WaitForChild("TextLabel")

local function FireServer()
    game:GetService("ReplicatedStorage").ClickToTeleportEvent:FireServer(position)
end

tool.Activated:Connect(function()
    local position = mouse.Hit.Position

    if debounce == true then

        debounce = false

        FireServer()
        AnimationTrack:Play()
        teleport_label.TextTransparency = 0
        teleport_label.BackgroundTransparency = 0
        teleport_label.Text = "CoolDown: 5"

        for i = 5, 0, -1 do
            teleport_label.Text = "CoolDown: " .. i
            task.wait(1)
        end

        teleport_label.TextTransparency = 1
        teleport_label.BackgroundTransparency = 1
        teleport_labelText = "CoolDown: 2"

        debounce = true

    end 

end)