In Windows / Firefox ... it is common to open the search with ctrl-f and to find the next item with F3 ...
Changing the shortcut to F3 did not work in Linux Mint ...
WFM
Works for me too, Xubuntu 18.10 unless the Find dialog is focused, in which case it doesn't work for me also, but just pressing <kbd>Enter</kbd> multiple times works fine.
You can set that in keybindings: `Preferences > Keybindings`, section `Search` and there you can set `Find Next` to `F3` and possibly `Find Previous` to `<Shift>F3`
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