GetPlayerFromCharacter doesn't work?

The reason this is happening is because GetPlayerFromCharacter returned nil, because char was actually the Workspace, or some other Model that touched the part. In order to fix this, you will have an if statement that checks if the player exists.

local blueFlag = workspace.BlueFlag -- don't repeat yourself! Have a variable for blueflag

script.Parent.Touched:Connect(function(hit)
    local model = hit.Parent -- use local variables! usage of global variables is bad practice 
    local player = game.Players:GetPlayerFromCharacter(char)

    if model:FindFirstChild("BlueFlag") and player then -- if there is a player 
        char.BlueFlag.Parent = game.Workspace
        player.leaderstats.Points.Value = player.leaderstats.Points.Value + 100
        blueFlag.RemoveWeld:Invoke()
        blueFlag.Position = Vector3.new(69.5, 0.5, 40)
        blueFlag.Anchored = true
    end
end)