You can manually create custom searches as regular bookmarks with a keyword so they should sync.

I'd also like to know this. Been using Firefox mobile but chrome on PC and syncing custom search operators could be what gets me to switch back to FF on PC

> Do they sync with Firefox Sync?

No.

> Do they work on Firefox for Android?

Yes.

I think akvadrako above[1] has it right, they appeared on my mobile phone on sync, as they are bookmarks.

Again, I think, I'm not sure ;)

[1] https://news.ycombinator.com/item?id=22115461

There are two things being confused here.

I was thinking about OpenSearch custom search engines (being deprecated apparently as another comment notes, these appear on desktop as icons under the search input field "This time search with" and similarly in Android as icons above the on-screen keyboard. These definitely don't sync.

The other thing are bookmarks with the "keyword" property set. These do indeed sync, like other bookmarks.