I think all of your choices work well but my favorite is [name_f]Nora[/name_f]. I like that both are classic former nicknames that have become stand alone names.
[name_f]Emma[/name_f] & [name_m]Jack[/name_m] are also great together, as are [name_f]Ella[/name_f] & [name_m]Jack[/name_m]. I like them all, but these are my top three.
From your list [name_f]Kate[/name_f] probably fits best with [name_m]Jack[/name_m].
I suggest the name [name_f]Susie[/name_f] or [name_f]Suzi[/name_f]. It’s classic and cute and not frequenting used right now.
My favorite is [name_f]Nora[/name_f] but I know multiple siblings [name_m]IRL[/name_m] named [name_m]Jack[/name_m] and [name_f]Emma[/name_f], so I think those names go wonderfully together!
[name_f]Kate[/name_f] is perfect with [name_m]Jack[/name_m].
They’re sophisticated, spunky four-letter nicknames for “core classic” names – the most classic of classic names – [name_f]Catherine[/name_f] and [name_m]John[/name_m].
Additional sibling ideas for [name_m]Jack[/name_m]: [name_f]Annie[/name_f] (nickname for “core classic” name [name_f]Anne[/name_f]), [name_f]Meg[/name_f] (nickname for “core classic” name [name_f]Margaret[/name_f]) and [name_f]Libby[/name_f] (nickname for “core classic” name [name_f]Elizabeth[/name_f]).
My favorite is [name_m]Jack[/name_m] and [name_f]Emma[/name_f]. I also like [name_m]Jack[/name_m] and [name_f]Annie[/name_f], [name_m]Jack[/name_m] and [name_f]Daisy[/name_f], and [name_m]Jack[/name_m] and [name_f]Susanna[/name_f].
I like [name_f]Ella[/name_f] and [name_f]Hannah[/name_f].
Other suggestions would be :
[name_f]Lillian[/name_f]
[name_f]Josephine[/name_f]
[name_f]Celine[/name_f]
[name_f]Clover[/name_f]
[name_f]Faydra[/name_f]
[name_f]Phoebe[/name_f]
I love [name_f]Nora[/name_f] to go with jack as [name_f]Nora[/name_f] is quite un used at the moment which makes the name more special. Other suggestions [name_f]Millie[/name_f], molly, [name_f]Maisie[/name_f], daisy, lily, [name_f]Rosie[/name_f], [name_f]Emily[/name_f] are all pretty names too if you like classical kind of names