I found this user who has posted four spam posts in the Discussions tab of the Mobile Development Collective. I’ve flagged all the posts.
Do I need to do anything else?
Also, what measures have been implemented to stop such a wave of spam by a single user?
I am mostly going off of this answer by Machavity. Although that post is generally concerned with self-promotion, the same principles apply (not necessarily for the same reasons).
Moderator flags are necessary for patterns
If a user is making lots of posts, understand that moderators work on a post-by-post basis. Sometimes you'll get lucky. I've come into the console and seen a large number of spam flags pending and realized they are all for the same user. Do not rely on that. Moderator flags tell us what we need to be looking for, and they are the only reliable way to alert us to patterns.
Dealing with Discussions flags suffers from a lot of limitations, even compared to the imperfect tools on Q&As. Discussions Moderators (and Diamond Moderators) only see the list of flags (and a summary of each page, thanks to Henry Ecker's userscript) and ultimately much less information is exposed. As Machavity points out in their answer, if a post gets nuked by community's flags or if the pattern is missed for other reasons (e.g. different mods handling the flags), the abuse will most probably go unnoticed. Especially considering the fact that we are still waiting for Charcoal's API to be functional in Discussions.
All that said, I'd recommend raising a custom flag (it suffices to be raised only on one of the posts; the rest can be flagged as spam) and mentioning the pattern (links are appreciated), so it can be dealt with appropriately (e.g. diamond mods have been helping by nuking the accounts of repeat offenders when it was brought to their attention).
