The flesh is the carnal mind that can not discern spiritual things.
Actually, flesh is the experience that inflicts the mind (spirit) with temptation. "spiritual things" is another concern altogether. I'm talking about discerning between good and evil and we all have that capacity because of Christ. We all have the light of Christ in us. We don't need God to tell us that it's wrong to kill someone else or to take their stuff or lie about them. This understanding is born in us. Christ is written in all of us, not just you guys.
So, when you talk about flesh or the carnal mind, it has nothing to do with discerning "spiritual things". It has to do with choosing evil over good. Some people do it for fun. Some do it to get gain. Some do it because they are pure evil. And, some do it for temporary gratification that they sometimes get addicted to. They all know they shouldn't, but their carnal nature allows them to excuse themselves. This is true with everyone including born-again Christians.
The difference between a Christian and everyone else is that the Christian has accepted Christ and claims they are living by His teachings - it doesn't matter if they are. It only requires that they claim that they are. The mode of modern Christianity seems to be, don't worry about your sins, God has paid for all of them including the ones you haven't yet committed. That is an extremely destructive doctrine. It is exactly the opposite of the gospel message.
The gospel message calls for repentance. The sinner must repent.
The doctrine you offer calls for God to forgive the sinner. God must repent only because the sinner said, "I believe!".
As for "spiritual things", that is the ability to discern truth and it just doesn't look like you guys have any of that ability. You all spend so much time working around the truth, the plain and obvious truth, that it's obvious discerning truth doesn't exist among our critics. They won't even address the issues. They spend most of their time deflecting rather than addressing the questions. One prime example is your response. You made a bold statement that obviously crosses lines. I pointed out the issue and suggested that you might want to reword your statement and you still press forward, apparently, believing you've not made a mistake.
How can we do anything if the Spirit is not at work in us?
Your question crosses boundaries. It's a lame born-again Christian talking point that makes no sense at all. We can do many things when the Spirit is not at work in us. So, I'll ask you again if you want to reword your question to ask what you really meant to say.
I'll pose a more pointed question. Is it possible for men to do good works without the Spirit working in us? (This naturally assumes that men can do some things without the spirit. That's a concept that your question excludes and makes it so that only your ilk can do good - a laughable concept.)