Attempt to index nil with Parent?

The problem is that it can't find the parent of the game.

script.Parent = ServerStorage script.Parent.Parent = game script.Parent.Parent.Parent = nil

And you're also trying to find the player's humanoid inside server storage, which humanoid is not one of server storage children.

Fortunately, we can use the data from the first script to get the player's humanoid using remote events.

No changes need to be made except pasting the script.

First code:

local remoteevent = Instance.new("RemoteEvent", game.ReplicatedStorage)
remoteevent.Name = "BurnEvent"
local cool = false
script.Parent.Touched:Connect(
    function(hit)
        if hit.Parent:FindFirstChild("Humanoid") and cool == false and hit.Parent ~= script.Parent.Parent.Parent then
            if hit.Parent.Humanoid.Health > 0 then
                cool = true
                if game.ServerStorage:FindFirstChild("Burn") then
                    local burn = game.ServerStorage.Burn:Clone()
                    burn.Parent = hit
                    burn.Disabled = false
                    if burn ~= nil then
                        wait()
                        if hit.Parent.Humanoid.Health == 0 then
                            local name = game.Players:GetPlayerFromCharacter(script.Parent.Parent.Parent)
                            if name:FindFirstChild("leaderstats") then
                                name.leaderstats.Kills.Value = name.leaderstats.Kills.Value + 1
                                name.leaderstats.Coins.Value = name.leaderstats.Coins.Value + 1
                                emoteevent:FireServer(hit)
                            end
                        end
                    end
                end
                script.Disabled = true
                cool = false
            end
        end
    end
)

second code

local remoteevent = game.ReplicatedStorage.BurnEvent
remoteevent:OnServerEvent(hit)
while script ~= nil do
    wait(0.1)
    local check = hit.Parent:FindFirstChild("Humanoid")
    if check then
        if hit.Parent:FindFirstChild("Humanoid").Health > 0 then
            cool = true
            local wa = Instance.new("Fire")
            wa.Parent = script.Parent
            for i = 1, 5 do
                hit.Parent:FindFirstChild("Humanoid").Health = hit.Parent:FindFirstChild("Humanoid").Health - 10
                wait(1)
            end
            wa:Destroy()
            script:Destroy()
            cool = false
        end
    end
end