I don't think that Vermouth being the Boss' favorite can be a solid evidence to conclude about his/her gender. Not only that it doesn't necessarily have to be a romantic interest, but it can also be a clever trick that Gosho uses to mislead us.
We always think that for some unknown reasons, the Boss likes Vermouth, therefore allows her some independence. But what if the truth is actually the whole opposite ? I.e. The Boss doesn't really want that willingly...
POSSIBILITY #1: Vermouth blackmailed the Boss into allowing her certain powers.
In other words, the whole "favoritism" thing is just a cover to fool the other BO members and to protect the "pride" of the Boss. Only the Boss and Vermouth know the truth.
Vermouth might have known/possessed something that was to the Boss' disadvantage. But for some reasons, he/she can neither kill nor threaten her, thus had to give her some independence and high-ranking to her request, so she can keep her mouth shut.
POSSIBILITY #2: Vermouth is the "mother-figure" to Anokata.
This theory's solidity depends on Vermouth's and Anokata's true age.
Vermouth may not be the Boss' biological mother, but she might have been the one to raise the Boss ever since he/she was a child. Therefore, The Boss has to treat her with more respect (and probably less power) than the others, even when he/she doesn't want to do it willingly. This also explains The Boss' seemingly phlegmatic attitude towards Vermouth's potentially dangerous behaviors (e.g. being secretive).
POSSIBILITY #3: The Boss is not who we usually think to be, thus doesn't have enough power, so Vermouth just takes advantage of this.
(See Chekhov's theory above)