Let me start by saying "good to you for looking after your nephew and his grades." Taught for over 30 years, so let me give you some advice.
1. You need to talk to your sister, his mom, without her consent, you can not access his school records. So go to her and tell her about your concerns, and that you need her to call the school, and add you as a contact for the child and its ok for you to see his grades and so forth.
2. You then need to call the school, make sure your sister had already called, tell them who your are, and your concern, give them you name, email and other information. Tell them you want to be able to access their grading program so you can exam his grades. Schools generally use one of two programs Power School or JMC, find out which one, and ask if assignments are post online and if so where? Schools use a variety of systems but many use Google classroom. Be sure you get the code to log into the system.
3. Once this is done you should be able to access his grades, do so and find out who his teachers are, you can get their email address through the school website. He may have anywhere from two to 6 core class teachers. Once you find that out, send them an email. Do NOT call them, we are busy enough the way it is, tell them who you are, voice your concerns and ask them why they think the child is struggling, be sure to include that all of this has been approved by the mom and office, and they are free to check. Be sure to tell them you want to help. tell them you want to be informed by the grade program when any assignment is given.
If any teacher does not get back to you in a couple of days, send another email and again wait 2 days, after that email them a 3rd time along with the principle.
Few kids these days fall through the system by 6th for getting checked for ADD or ADHD,
Now comes the hard part, you have to be the parent and tell him, you have access to his grades, and assignments, and want to know why they are not getting completed. By 6th grade they have homework, maybe not nightly but at least 2 or 3 times a week per class. Be the adult, look daily and if you see that he has been given a zero, email or text him and find out what is going on. You have to be a pain in the ass to him. He is going to ask "why do you care, you are not my dad and the rest of it." Stand firm, and just tell him, "we do not raise losers in our family, and we are not starting now. "
I would say its already getting late by 6th grade, he is already behind his classmates and it will just get worse. You need to act now, or forget it, because by 8th/9th grade he will be too far behind to ever catch up.
Good luck and go CYCLONES.