Wow, really? I trashpicked an old Brother multifunction, and whatever provides the printing service on Ubuntu just found it automagically. I had to download a .rpm to get the scanner working, but it was right there on Brother's website. Years old, but worked flawlessly.

I've got a Brother MFC L2710DW that both Linux and ChromeOS print to without any trouble at all. Newer Chromebooks with the Google Playstore also give you access to the Brother Print & Scan app, which also works.

Huh, we have a Brother HLL2390DW multifunction laser, and I can't figure out how to set it up on ChromeOS at all. There's no working driver as far as I can tell.

The Print&Scan app is a disaster, largely due to how Android works on Chromebooks. It can only access the totally separate Android filesystem, which isn't visible in the ChromeOS Files app. If you want to export a scan to the ChromeOS files, you have to use the "Share" button and pick the Files app. You can't use the very prominent "Save" button.

They don't provide handy-dandy single-click driver installation tools for Linux, but I'm not aware of any printer manufacturer that does. However, Brother printers do use standard protocols, so if you can find the PPD file for the model number, all you need to do is provide that to CUPS and it should Just Work.

They provide CUPS drivers even for my $50 HL-1112 "Windows Printer" (you know, one of those that doesn't have built-in PCL or processing, it needs everything rendered on the PC). I know the networked ones are even better.

Not using ChromeOS though so can't comment on that.