I'm pretty sure that won't work in firefox.
Things that can break page-break are(using page-break inside)
- tables
- floating elements
- inline-block elements
- block elements with borders
To define if a break must be done, the following rules are applied:
1.If any of the three concerned values is a forced break value, that is
always, left, right, page, column or region, it has precedence. If
several of the concerned values is such a break, the one of the
element that appears the latest in the flow is taken (that is the
break-before value has precedence over the break-after value, which
itself has precedence over the break-inside value).
2.If any of the
three concerned values is an avoid break value, that is avoid,
avoid-page, avoid-region, avoid-column, no such break will be applied
at that point.
Once forced breaks have been applied, soft breaks may be added if
needed, but not on element boundaries that resolve in a corresponding
avoid value.
break after - CSS | MDN
In short words, in your case cause you are using it inside flex
won't work.
break-after
which, however, is not implemented in any of the browsers yet. – Deadeye