I need to transfer a large amount of data between a wireless and a wired client through a Flint 2 router and a Slate 7 (connected via WDS), and the transfer clogs the whole network, including internet access. How can I circumvent this and make sure the transfer is restricted to a reasonable portion of the available bandwidth?
It depends which tool you use to copy it over.
Some tools have a way to limit bandwidth that is what I would do.
The problem is that wireless always have a higher priority than cable, so in the worst case scenario it can overtake all connections to the router over wire rendering things inaccessible.
Can you tell me more what kind of local transfer it is?, is it scp, ftp, net share.
Also there is a chance the router can lockup if multiple network switches are involved and hardware accerelation is active on the flint 2, this likely would happen in a situation the load and bandwith is too big to properly offload that it is dropping packets and checksums causing havoc with loop protection mechanisms like STP(treespanning protocol), you may try to disable it to see if it helps to some of the behaviour you describe.
rsync is used for the data transfer between a macOS host (wireless, APFS) and a FreeBSD (wired, ZFS, mirrored). The same transfer between two wired clients (Synology and FreeBSD) does not affect other hosts and/or the Internet connectivity.