His statement that "They fail to notice that, even should it be believed or demonstrated that the world is round or spherical in form" implying that he does not believe the "world" is round or spherical but flat. I completely admit that he held this opinion. The point is that he didn't hold it to such a high importance as to consider it Divinely Revealed, as evinced by his admission that the world being proven round is possible. The model is irrelevant to the issue of whether St. Augustine TAUGHT the flat Earth.
I've studied the Fathers trying to understand what the Fathers are saying here. From what I can tell, Augustine is addressing whether the world, (everything) is encased in a spherical cover where the top half is a dome, (attempting to answer whether heaven is spherical) that either the the heavenly star-containing dome encircled the flat earth around the bottom, or, was it strictly a dome that covered the top portion of flat earth while leaving the bottom half of earth outside. That is why he didn't consider it of much import. Either way, a dome (firmament) covers the top and meets up with the sides of earth at some point before proceeding around the other side, if indeed heaven is spherical. Or there's only a dome. Everyone seems to interchange terms to suit their understanding. But Augustine was a flat earther and when he said "world", as far as I know, he didn't interchange the term with "earth". As far as I can tell, when the Fathers discuss the heavens, universe, firmament, dome, or world, they are not talking about earth and vise versa. So the answer to your question is no. Augustine did not think the universe is flat.