When I see a spam answer, I flag it for moderator attention. Should I also downvote it?
Downvoting it is not absolutely necessary since the question would be deleted soon.
However it's fine if you downvote SPAM "questions", to quickly mark them as not useful, so other site users could see that it's not worth opening and reading.
Spam posts should be flagged as spam using 'flag' -> 'it is spam'. This way it is automatically down-voted by Community and will be deleted once it got flagged as spam often enough (I think six times, or so). Please don't flag it for any other form of moderator attention, except it requires immediate attention, e.g. something should be removed right away because the content is not tolerable (hate speech, porn, etc.).
You can also down-vote it yourself if you want. After the post got deleted you will get your -1 reputation back. But this is not required. The spam flag is much more important.
Yes. If something gets "enough" spam votes then it gets automatically deleted.
Oops, that wasn't quite the right answer. Sorry. Still, I think that that link is useful to know about.
I think that there's also a mechanism whereby if something gets enough downvotes quickly enough then it will also be locked and deleted, but I can't find that information on meta.SO right now.
Another reason for downvoting (and commenting) is that if it really is spam, this highlights the fact to other (non-mod/non-10k) users who can participate in getting the spam off the site as fast as possible (the point being that only mods/10k users can see the spam flags and so get notified of potential spam).