There is, currently, no need for a new "not in English" flag for answers.
Contrary to the statement in your question, there is no "Not in English" flag for questions.
There is a community specific close reason for "Not written in English", which was somewhat recently added. When a question is closed, there's a post notice showing specific information to the user as to why the post was closed and how the question author might edit their question in order for it to be reopened. There's definite benefit to telling users that they should edit their question to be in English using a dedicated close reason. It is possible for other users to either close-vote or raise a close-flag for the specific close reason of "Not written in English". However, unlike you have stated in your feature request here, it's not actually a "a flag called "Not in English" for questions". There is no such flag. There is a close reason and a flag for closure, which users with less than 3,000 reputation can raise. User's with more than 3,000 reputation can't raise close flags.
A Very Low Quality (VLQ) or Not An Answer (NAA) flag should be used for answers not in English, not an "in need of moderator intervention" flag.
You were using instructions contained in an antiquated answer. The correct instructions are in the answer to the FAQ question: "How do I deal with non-English content?". Those instructions are to use a VLQ flag, with NAA flags also being acceptable. An "in need of moderator intervention" flag that just states that the answer isn't in English is likely to be declined with the stock flag decline reason of:
Using standard flags helps us prioritize problems and resolve them faster. Please familiarize yourself with the list of standard flags: see What is Flagging?
Unfortunately, finding the correct instructions once you landed on the question you were looking at was complicated by there both being an inaccurate answer to that duplicate question and the duplicate targets on that question pointing to a confusing set of questions, including one that was merged into the actual FAQ question that holds the community maintained answer describing how such non-English content should be handled. I have deleted that inaccurate answer and adjusted the duplicate targets list for that question, and several other questions, to point directly to the FAQ "How do I deal with non-English content?".
Unlike a question close reason, there isn't any benefit to the answer author to having a separate "Not in English" flag.
Unlike question closure, there are no post notices telling users specifically why their answer was deleted. All such information is communicated through either a link to a general description of why answers might be deleted or contained in a custom comment on the answer. Thus, unlike closing a question for the "Not in English" reason, there would be no benefit to the answer author to having a specific "Not in English" flag.
While it would be possible to have a separate post notice for this answer deletion reason, it's a much larger ask to have that, because we then get into the issue of what other post notices should there be for answer deletion. That is something that could be/should be explored, but it requires quite a bit of work, including not just thinking about "what answer deletion post notices should there be", but also "how should it be determined what to use", etc. For example, would users in review queues need to specify a specific reason? Should > 20k users need to specify a specific reason when voting to delete? Should moderators need to specify a specific reason when voting to delete? How should it be handled when the reason selected is inaccurate? etc.