After the most recent chapter, what I am starting to think Kanki's weakness is, is perhaps an inability to accept any kind of loss whether it be a tactical loss or a personal one.
Bear with me now for I am going to get into the more spiritual side of Kingdom that some folk apparently dislike. Lol.
As I said before, whatever weakness Kanki has was never attributed to his army, his methods or his tactics but to himself as an individual.
Loss is a large part of how people grow in Kingdom (and in real life). The entire "Weight of a General" deal is rooted in an individual carrying on the legacies of those who were dear to them but in order to carry on said legacies, the character has to accept their loss in the first place.
I think Kanki's problem is that he cannot accept loss and I believe Hara alluded to this when Shin first met him.
Shin immediately noted something strange about Kanki when he first met him.
A "sense of rejection" was what Shin felt towards Kanki. Shin has dealt with bloodlust, crushing auras, Mangoku's ghosts and the Weight of Great Generals yet something about Kanki immediately set him on edge. What I think Shin unknowingly sensed was that Kanki is the complete opposite of him.
Shin obviously is all about the concept of "Weight", the whole deal of carrying around legacies etc. You know the deal.
Houken was the opposite of Shin in that he refused emotional attachments altogether. Kanki however is different from Houken because he doesn't reject emotional attachments as shown by how Raido's death has affected him and is now affecting his judgement.
Kanki (either knowingly or unknowingly) embraces attachment but cannot handle nor accept loss thus he ends up casting aside and "rejecting" the legacies of those that were close to him.
A person like that is exactly the kind of individual that Shin would detest and "reject" on an instinctual level.
Kanki even possibly goes so far as to project this weakness of his onto others, belittling others for supposedly not understanding how "grown ups do things".
In battle too, Kanki refuses to back down no matter what utterly insane odds are stacked against him yet he ultimately wants to risk nothing that is actually close to him. That is why he sent Ogiko to warn Raido not to do anything reckless and to sit back because he knew that Raido, who is arguably the only one of Kanki's inner circle that is genuinely loyal to the man hence why Kanki is probably attached to the bloke, would do anything to prevent Kanki's defeat.
Kanki is a character that we have never gotten to truly know so far. Kanki masks his inner self with an aura of charm and confidence that he wears like a glove, though his charm is arguably superficial and now his confidence has been tested and appears to have broken instantly.
Essentially, Kanki is acting like a child because he is one. He is someone that has never matured and can neither handle nor accept genuine loss. He hates losing and cannot stand being defeated in battle nor losing those he cares for despite his inherently dangerous occupation of being in a literal army.
What we are now witnessing with Kanki is not character development or character change but rather a character reveal. We are finally seeing the real Kanki that is deliberately hidden beneath layers of superficial charm, smug arrogance, brittle confidence and inflated ego.
If all that sounds like a rather ugly combination, well... Hasn't Kanki been built up to be a rather ugly individual?