Asking for feedback is (almost) always a positive endeavour. It lets your users know you care about the quality of your content and service, and that you value your users' opinion.
If you don't ask for feedback, the only way for a user to let you know they like or don't like something, is through a coincidentally well time survey. More often than not, they won't do anything. That only happens if the problem is so serious they'll contact your support service. But for the minor annoyances and issues, your user will ignore the problem or give up.
Giving feedback for accuracy is a pattern you'll find in many FAQs and/or help articles. Instead of using a flag, which is a negative symbol for reporting inappropriate content, you could use a monicker like 'was this helpful? YES/NO' and then provide options to why the user believes the content was not accurate. In your case, a 'how can we make this article better for you?' might be better.
You can display a multitude of predefined options to process common complaints, or let users freestyle their feedback. Since you're dealing with a very specific userbase and rather detailed feedback, you may want to use a textbox. This will be more work for you to process the feedback, but you'll be able to do more with it. If you decide to go this route, do let users know you value their time and that you will use their feedback to improve the service. Optionally you can ask for their email address to give them a heads-up for when the content has been changed, or for more details.
It's important to keep the feedback form low entry; if you ask too many things or too complex questions, you risk making the user feel like they have to do actual work. So make sure the feedback box is as simple and easy to use as possible, or you’ll be missing out on the feedback that it was designed to catch.