@.access:
Maybe he is not found out in the moment, but eventually Big Mom will know. Maybe she only finds out Luffy was the one who kidnapped Sanji after he takes Kaido down, that's possible, but then what? Regardless of how long it takes for BM to blame Luffy on this, once she does, the innocent ones the SH know will be targeted by her and Luffy can not afford it. It's not like he has an spy on her crew who can report to him when she finally finds out he is guilty. It will be like leaving a tickling bomb away that will explode at any minute in the hands of innocent people the SH love.
Not to mention: how will Luffy track BM down later? Even if she doesn't find out he is guilty until he takes Kaido down, how he will attack her before she does anything? Pekoms will not be around to guide him to her then. She will have the initiative either way.And regardless of all that, BM doesn't need to know it was Luffy who kidnapped Sanji in order to attack the ones related to Sanji. As soon as Sanji disappears, I am pretty the ones close to him will be targeted anyways. Unless they find someone to impersonate him… Where is Duval now?
It would be indeed the best if Luffy somehow took out Big Mom before going after Kaidou, but would need to be "subtle" about it (i.e. not start a big war).
He would require an actual plan instead. Something to weaken her forces.
–- Update From New Post Merge ---
@uniaka:
I think the most seif place for SH now is at Big mom 's land. Would Kaidou attack them knowing he is going in Big mom's land, that likely are bigger enemies and SH and Big mom? Going to big mom could help get Kaidou out of their back.
Don't think Kaidou cares. He tried to pick a fight with Whitebeard, remember?