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If I put "\M-\C-k": kill-whole-line in my ~/.inputrc file the result is "\213": kill-whole-line (displayed by bind -p).
However, if I change \M- to \e ("\e\C-k": kill-whole-line), the key binding works as expected.
How can I use \M-\C- ("meta-control") as a prefix, when defining key bindings using Readline in bash?
You can't use \M- because it's broken. Keep using \e for the Meta/Alt prefix.
Using \M- in readline bindings does not work reliably with terminal emulators which prepend an ESC (\x1b) character instead of turning on the high bit when Meta/Alt is pressed and/or with UTF-8 locales (both of which are generally the default on most modern systems [1]).
With some versions of bash (e.g. 5.0, but not the newer 5.1), using \C-\M- works differently from \M-\C-, so just using \C-\M-k instead of \M-\C-k may actually do what you want -- until the next update ;-)
bash-5.0$ bind '"\C-\M-k": shell-backward-kill-word'
bash-5.0$ bind '"\M-\C-k": shell-kill-word'
bash-5.0$ bind -p | grep -a shell-.*kill-word
"\e\C-k": shell-backward-kill-word
"\213": shell-kill-word
[1]: not with xterm though, where you would need something like XTerm*VT100.metaSendsEscape: true in your ~/.Xresources.
\M- is only usable with terminal emulators which are configured to use legacy 8-bit (non utf-8) encodings and to turn the high bit instead of prepending an ESC when Alt is pressed. But there are zero reasons to use that config nowadays, and it's not the default anywhere.