Install a browser extension that replaces web-page emojis with Twemoji (or another emoji set that includes flags).

Example: Twemoji for Chrome (or Emoji Swap) — installs web fonts that render flags.

Chrome Web Store

Restart the browser.

Open the site where flags were missing — they should now show as colored flags (Twemoji supports country flags).

If one site still shows letters, it may be using embedded images or its own emoji renderer — browser extension won't fix that specific app.