Flexbox is by no means necessary to make a responsive web page. Media queries have been supported by mobile browsers for over a decade as has the viewport meta

Flexbox is by no means necessary to make a responsive web page. Media queries have been supported by mobile browsers for over a decade as has the viewport meta tag. Between the two it should be straightforward to make most page designs responsive. Old browsers (old IE especially) that don't handle those features aren't a problem because they'll just fall through to the screen style. Trying to use JavaScript to help old browsers is a worse solution as you're more likely to run into JavaScript incompatibility problems than CSS.