A large number of users doesn't seem to know about the correct way to deal with obvious spam. They might just downvote the spam or flag it as "not an answer" while the by far fastest and most efficient way to get rid of the spam is to flag it as spam and trigger the auto-deletion.
I propose that on posts with at least one existing spam flag, if you take any negative action like downvoting or flagging a notice is displayed asking if you agree that the post is spam. If the user clicks yes, this triggers a spam flag from that user.
In the case of flagging, instead of a notice one could also just put the spam flag pre-expanded at the top of the flagging dialog.
This notice could also educate users about spam flags at the right moment when they are encountering a spam post.
To avoid misuse by making the spam flagging option too prominent, it might make sense to only enable this for 1 rep users and disable this feature when the spam flag is disputed by any user.