facebook intentionally doesn't open access to these things; so aside from "highjacking your browser, scrolling and downloading in a scripted manner", this might be hard (and that solution would not be easy to use). Software developers (especially of the popular Pidgin multi-platform chat client) have been playing cat&mouse with Facebook's attempts to shut out third party clients, and I think Facebook finally won.
So, I don't think there's an easy solution to your problem. There might be solutions for other chat protocols, where you as the user get to choose the chat client with which you connect to the network, instead of the network dictating how you do that. (Such options would be Telegram, Signal or Matrix.
In absence of a solution for the Facebook chat, which I think would be the preferable choice for your family, I can only outline how things would work with an alternative. I don't know whether that's helpful for you, if it's not, just stop reading here, and focus on the negative answer I gave above, please.
At least for the Matrix chat system, the popular Element client for Matrix has a button that lets you download a selectable frame of messages, including the attached files. Maybe give the Element App a try on your Android or iOS phone/tablet, or try it in your browser; you can use your Facebook account to log in, so you don't need to remember a new password (you do need to pick a user name). It doesn't do "discovery by phonebook", so you need to explicitly sign up and invite people by their usernames, but that's not hard.
If you think that hey, you're the one who'll be doing the backups on your PC, but your uncle really shouldn't bother with an interface that has this option, as it might confuse him, FluffyChat does a surprisingly good job at keeping out of people's hair.
