Kyoshiro could possess the Snake-Snake Fruit, Cockatrice/Basilisk Model, a Mythical Zoan Devil Fruit.
The Cockatrice is basically a lizard with a rooster head. The wings can either be rooster wings or dragonesque wings.
I’ll split the rest of the post into why Kyoshiro has this fruit.
1. Kyoshiro’s design fits pretty well with the Devil Fruit given his stature and his ridiculous pompadour which could easily meld into a Rooster comb and his eyes which are even more important for the reason below
2. The primary ability associated with the Basilisk is a death stare. It can vary from the Basilisk killing someone just by staring at them or just completely paralyzing them by staring at them. And Kyoshiro’s most outstanding physical attribute is his eyes and stare.
3. The usage of the Basilisk in prose and myth aligns well with Kyoshiro’s personality and usage in this arc. The Basilisk represents treachery and being vertigo venomous. It’s basically all the common attributes of snakes but amped up to 100 and Kyoshiro has displayed both through his apparent remorseless cutting down of Komurasaki and later lying to Orochi about her not actually being dead. This also aligns with the choice of Orochi’s DF where the use of Yamata no Orochi in myth is that of a glutton and power hungry figure, like Orochi.
4. The usage of the Basilisk in popular fiction also aligns well with Oda’s agenda. This arc is full of references to Samurai films and even old Samurai anime such as Rurouni Kenshin, especially when it comes to Zoro. So it’s fitting the first actual Wano Samurai Zoro faces is Kyoshiro with a Basilisk fruit, similar to how Kenshin’s first big fight was with Udo Jin-e, a character with basically this exact power of paralyzing people on sight. Also this power is the main ninja technique in the fantastic classic anime known as Basilisk so Oda could reference that too.
5. This power from the Basilisk fruit can potentially also explain how Komurasaki didn’t die after everyone saw her get cut down. Kyoshiro with such a power could paralyze Komurasaki’s organs and blood vessels preventing them from further bleeding even after he cut her. So Komurasaki was basically suffering the equivalent of only a flesh wound or even a mere scrape according to how fast and deep Kyoshiro applied his Basilisk powers despite the initial bleeding we see.
6. The last reason is obvious. All the top antagonists in the arc seem to have Zoan fruits and since some people are putting Kyoshiro as a bigger threat than Orochi now, it would follow suit that he also has a Zoan fruit.
*Theory by ImmaIvanoM