What's the meaning of "leave someone or something flat", or here in this sentence: "Leave the old bag flat since it has a big hole"?

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To leave someone flat means to abandon someone without caring about what happens to them and without providing them with any resources (money, transportation, etc.).
"My boyfriend and I had a fight and he just got up and left the restaurant, leaving me flat. I didn't have money to pay the bill or a way to get home."
"My business partner took all of our money and fled the country. I was left flat with a pile of bills and no way to make the payroll."
It can also mean to do something in a way that leaves them unimpressed, unamused or disappointed.
"Thomas gave a presentation in the business meeting, but it left us flat. No one was impressed."
Your sentence, about leaving a bag flat, is confusing and not natural. I think it means not to pick it up or to try to use it because it is worthless. Just leave it there. But it is an odd sentence, IMO.