In the ensuing days, I frequently invited him to accompany me to flee the school when one of my board game friends doidn't want to stay in the school.

They (every time, I invited a person, so they denote the aggregate of personmultiple people) usually firstly asked me, " If I want to get away from here, but how?

I excited toly shouted," hHow do you know it can't be scaled if you even don't try to do it, and if you want freedom, please chase it."

But they almost refused, the last words they said to me was, "I can't afford it."

The movie said, "sSome birds aren't mean to be caged, their feathers are just too bright."

In the ensuing/following days, I frequently invited him to accompany me to flee/escape the school when one of my board game friends doidn't want to stay in the school.

The "following" days is much more commonly said.
"Flee" usually means running away from something that can chase you. Escape is a better fit.
The sentence is past tense, so don't -> didn't.

They (every time, I invited a person, so "they" is to denote the aggregate of personmultiple people) usually firstly asked me, "I want to get away from here, but how?"

"I said," w "When you go home at night after self-study at night, do you see the wall on the way to the school gate.?"

They replied, "Yes (I know it), but the wall is too high to be scaled, l. Likewise, we werould be dead if we weregot caught."

The people are answering a direct yes or no question, so it's natural to reply "yes" rather than "I know," but you could add "I know it" if you want.
Hypothetical situation: we would be (future possibility) dead IF we got caught (past tense, from the perspective of the future, possibility)

I excited tompassioned, I shouted," hHow do you know it can't be scaled if you neven don't try to do it, ar even try? And if you want freedom, please chase itdon't give up."

Excitedly shouting implies you are full of energy in a happy way. This speaker is moved by other strong feelings, so impassioned works. It is rather formal but your text is generally written formally, so it suits your writing.

Don't give up is a more natural alternative here.

But they almost refused, the last words they said to me were, "I can't afford it." / "I can't take the risk."

"Afford" is used in reference to cost. Typically for money, but it can be for something abstract. It isn't clear to me what the people can't afford. I wrote a more clear alternative (the risk of getting caught).

The/A movie (once) said, "sSome birds aren't meant to be caged, their feathers are just too bright."

Did you reference a movie earlier in your story? If not, you should introduce it (even just with "a movie once said")

In fact, this invitation is my imagination, and I think only this can reflect the value and cost of freedom.

Could you explain further? I don't understand this sentence.