Welcome to the forum. As far as your duties as Advancement chair, there are no special requirements except maintaining advancement records of the information from the boy's handbooks, keeping track of when they have fulfilled the requirements, recording the information with the local council, buying the patches and making sure they are ready for presentation at the Court of Honor. That usually involves SM and SPL signature in some cases. A check of the Blue Cards and validating that information is also necessary for the MB's. That information will not necessarily be in the scout's handbook.
I did this job for years, it's really just a lot of paperwork, but it's not that hard. There are a couple of different software packages, including the BSA software that has made the job a lot easier than it was 30 years ago.