The character recently has been having problems at schools. He got called by the teachers and he however denies to them he has been having problems.
Then he talks to a friend and tells him this.
My understanding is akin to "If I get thought/If I become feed up with this, I only need to take a short break".
Then he explains he's used to not going to school or not having friends anyway.
This said, I don't see why he used だけだし here?
I think that rather than the duration of the break,
嫌になったら休むだけだし
means "If it gets unpleasant, I just/only skip school, taking 休む in the sense of "not attending school/job, to be absent" (see 1. and 4. here) specifically, rather than "resting" in general.
I feel that だけ here adds the nuance that the speaker means he or she is NOT doing other bad things (such as engaging in a gang, vandalism or whatever) besides skipping school, he or she only skips school and that's it.
