It's not bad, but IMO it needs some work. I'd prefer Push/pull/legs where your shoulders are divided between the two upper body days so you can devote a day to just lower body. Also, don't forget to have rear-delts included in shoulders! Besides that:
Monday: Can you not do regular squats? I'd recommend back squats followed by either front squats or leg press, then glute-ham raises, leg curls, and calf work. IMO that's kind of what a leg day should look like.
Wednesday: Okay. If the volume for pullups/chinups is low I'd recommend perhaps adding in db rows.
Friday: Fine, although I'd personally prefer doing another compound on this day, e.g. CGBP or DB flat/incline press in place of flys or pulldowns. But if you really like both of those exercises, then by all means keep them in.
Ok I've added in what you've specified. I have to do Front Squats as the Gym I go to has no Squat rack and their is no gym nearer that has one.