The general rule is that you should flag for moderator attention only if there is something that you can't handle yourself. So ideally, with your new privileges, you shouldn't need to flag anymore. Downvote and vote to delete.*
We have to remember that we're still a very small site compared to Stack Overflow in terms of reputation. On SO, the number of >20k users is much higher than here (we have 21, by the way). If you just downvote and vote to delete a non-answer, chances are it'll go unnoticed and then stay around forever.
So please, just flag answers that aren't answers like you did before.
While this isn't official network-wide policy, I'm fairly sure the other SU mods would agree that we're not drowning in flags from >20k users, and thus will happily handle all your flags for answers that are eligible to be flagged.
If you want, throw in a vote to delete as well. If the review queues are being visited by 20k users, answers with pending votes for deletion might be prioritized, and the community could handle these things alone. I'm not aware of any example, but I've had Not an answer flags on posts with two pending delete votes from our higher reputation members.
To summarize, as long as we don't suddenly get a considerable number of (actively moderating) 20k users who use moderators as proxies for things they could easily handle themselves, there's no problem with the others flagging instead of voting to delete.
Finally, you can of course vote to delete any wrong answers that technically aren't eligible to be flagged, but might still need to be removed. This is something the community can do on its own.
* This is the rationale behind having users with vote to close privileges just cast their votes instead of flagging (see: How should my flagging change when I gain the ability to vote to close?).