An {index} placed inside an article can only include headings found in that article itself. It does not include headings from content outside the article, like modules.
Hmmm... It's strange.
I've edited FlexiContent item template and replaced </article> at the bottom of the page, to get more H2 and H3 in Quick Index. But it didn't work.
P.S. OK, I've removed <article> tag from the page at all - no effect.
Which tags Quick Index uses to detect article body?
I need to fix this problem.
Quick Index - like pretty much all plugins - gets the content of the article passed to it. It then does its magic on that content. After all plugins have done their thing on the article, Joomla pushes it into the template (HTML).
So the moment Quick Index sees the {index} tag, only the content of the article is available to it. Not the content outside the article.
For the {index} to work on other content below it too, the {index} would have to be outside the article itself. So it could be in your template file above where the article (component) is rendered.
It will then get handled in a later stage, when the entire HTML is known.
But then it would also include any headings found in content (modules for instance) that are found further on in the HTML output.