Because Brother drivers are not open source, they will never be included in Synaptic.
The best way to install a Brother driver is using a driver installer downloaded directly from Brother's site.
I do not know the model of OP's printer but this is where I download driver installer for my Brother printer. As you can see, Linux is fully supported.
https://support.brother.com/g/b/downloadtop.aspx?c=us&lang=en&prod=mfcj870dw_us_eu_as
I should have pointed out what I wrote above (how to install printer + scanner driver for your machine), but I thought you were having a problem with scanning function only.
At any rate, if anyone is in doubt, I vouch Brother (propitiatory) and HP (open source) are the 2 best printer manufacturers which give a good support for Linux.
You can ask @Karl how happy he is with his new Brother multifunction printer 