How do you stop this script from giving you like a thousand items?

You have nothing checking if the player already has the tool, here is what you can use:

local player = script.Parent.Parent
local backpack = player.Backpack

player.CharacterAdded:connect(function() -- Wait for the caracter to load
    if player:FindFirstChild("leaderstats") then -- Check for the leaderstats
        while wait() do -- Create a loop
            if player:FindFirstChild("leaderstats").Streak.Value >= 5 and backpack:FindFirstChild("minigun") == nil then -- Check for the streak and if they don't have the minigun
                game.ReplicatedStorage:FindFirstChild("minigun"):Clone().Parent = backpack -- Give the player the minigun
            end
            if player:FindFirstChild("leaderstats").Streak.Value >= 10 and backpack:FindFirstChild("AC130") == nil then -- Check for the streak and if they don't have the 
                game.ReplicatedStorage:FindFirstChild("AC130"):Clone().Parent = backpack -- Give the player the AC130
            end
        end
    end
end

If this worked please vote up and accept as answer!

~ Aaron