Ctrl+R (to paste from register) is failed in detached FlyGrep. I'd expect ^R to work as in any other window, to paste from some register. I guess "detach" script is not copying some "iedit" modules into detached plugin (see error text in screenshot below).
tmp_dir=`mktemp -d`
git clone --recursive https://github.com/wsdjeg/FlyGrep.vim -- "$tmp_dir"
echo "se rtp+=$tmp_dir" > "$tmp_dir/init.vim"
nvim -u "$tmp_dir/init.vim" '+FlyGrep' # type some text then and press ^R
rm -rf -- "$tmp_dir" # cleanup
After pressing Ctrl-R (after entered some text):

this feature is still wip
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