OK I configured my system as described in these two FAQ links:
https://support.displaylink.com/know...hen-displaylin
and:
https://support.displaylink.com/know...plication-only
Note that (a) I don't have an NVIDIA card, and (b) I'm using Ubuntu 18.04 while the latter FAQ entry says the screen freeze was in Ubuntu 17.10 and fixed in 18.04. Indeed I didn't have the screen freeze problem but that fix also appears to solve the flickering mouse issue.
Anyway, after rebooting with the above two changes, Slack no longer causes DisplayLinkManager to chew up my CPU like it did before.
I have not fully tested things but I'm hopeful things work now.