Hi,
Welcome!
I would second that he definitely won't be the only child who can't do these things! The video Ben shared is great and several children in my class use that technique. I would suggest that if you do that as part of it you get your son to check behind him. Cloakroom spaces are often small and it's very easy for a child to 'swipe' another with their coat as they turn it over their head.
The adults in school absolutely will support with these things but building independence is a key part of being at school and you can help a huge amount with that at home in lots of ways. Just saying 'have a go yourself first' to your child is a great start. Then 'I'll start the zip off and you can finish it'. Also giving specific pointers and praise for them so rather than just praising the zipping up maybe praise 'You held your coat at the bottom, that makes it much easier, well done.' Making your thinking out loud can also help - there are so many times as adults we just do things and don't realise the many steps/thoughts we have to help us achieve those things. For example talking through your own choices e.g. "It's raining so I'm definitely going to need to do my coat up, let me put the things in my hands down first so I can hold the zip properly. It's fiddly because it's small so I might need to try more than once."