For first, :connect is deprecated. Use :Connect

You need to use a "For loop", for get moderator use generic for loop. example:

-- Generic for loop

-- Basically generic for loop have "index,value" the value is the string stored in a table, and index is "string position", example:

local Table = {"String1","String2","String3"}

 -- also you can use: i,v
for index,value in pairs(Table) do
    print("The index is: " .. tostring(index) .. " The value is: " .. tostring(value))
end

local moderators = {"Player1","Player2","Player3"}

game.Players.PlayerAdded:Connect(function(Player)
    -- if you use _,... or ...,_ the _ is a nil value, after you put _ you can't use this.
    for _,moderator in pairs(moderators) do -- Generic for loop, getting all strings in table
        -- if you use print(_) this return nil.
        if Player.Name == moderator then -- Check if Player Name is equal  to moderator name
            print("The player: " .. Player.Name .. " is a moderator!")
        end
    end
end)

For your script you can use this:

local Moderators = {"Sk3pticalR0BL0X"}  --Enter the names of players who can use the GUI.

----------------------------------
-- DO NOT EDIT BEYOND THIS LINE --
----------------------------------

game.Players.PlayerAdded:Connect(function(Player)
    for _,moderator in pairs(Moderators) do
        if Player.Name == moderator  then
            game.Lighting.KickGUI:Clone().Parent = Player:WaitForChild("PlayerGui")
  -- Lighting is not a good way to storage items, use ServerStorage for this.
        end
    end
end)

Wiki pages:

For loop

Hope it helped