Another possibility is that Orochimaru might take an interest in Naruto's new skills. He could try to either steal Naruto's power or turn him to the dark side. Orochimaru has always been interested in powerful shinobi, and Naruto's rapid progress under Shisui's training would surely catch his attention.
Maybe some of the members of the Uchiha clan who don't approve of Shisui training an outsider like Naruto. They could see it as a threat to their clan's secrets and power. Shisui would then have to protect Naruto from these clan members while still training him.
It could be some of the villagers who are jealous of Naruto's sudden growth under Shisui's training. They might try to undermine him or spread false rumors about him.
Well, it could be that Naruto, being neglected in the village, is noticed by Shisui. Shisui sees Naruto's potential and decides to train him in stealth and combat skills. Naruto then starts to grow stronger under Shisui's guidance, and eventually surprises everyone in the village with his newfound abilities.
The Akatsuki could still be the main antagonists. Since Naruto is being trained by Shisui, they would see Naruto as an even greater threat. His new skills under Shisui's training could put their plans at risk. For example, if Naruto becomes better at stealth and infiltration, he could disrupt their operations more effectively.
The Akatsuki could still be the main antagonists. Even with Naruto being trained by Minato and becoming godlike, the Akatsuki's goals of collecting the tailed beasts would put them in direct conflict with Naruto. Their powerful members, like Pain or Itachi, would pose a great challenge to Naruto, despite his new skills.
The World Government could still be the main antagonists. Since Luffy is getting stronger under Mihawk's training, they would see him as an even greater threat. They might send their top agents, like the Cipher Pol units, to try and stop Luffy's progress.
The main antagonists could also be a group of rogue ninjas who have made a pact with some meta - humans from the Flash's world. They could be after Naruto because they want to use his connection to Barry Allen to gain access to the Speed Force. These antagonists would be a combination of the stealth and trickery of ninjas and the super - powers of meta - humans. They could create a lot of chaos in both the Naruto and Flash worlds, forcing Naruto to use all of his newly acquired skills and powers to stop them.
In such a fanfiction, Naruto might become extremely powerful under Kakashi's training. He could learn new jutsus faster and gain better control over his chakra. Maybe he'd also develop a closer bond with Kakashi, different from his relationship with Iruka or other characters in the original story.
Well, in this fanfiction, the Akatsuki could be the main antagonists. They would view Naruto's godlike powers as a major threat to their goals. Since Naruto has been trained by Shendu, his abilities would be unpredictable and extremely powerful. They might band together to try and take Naruto down. Additionally, there could be some ancient demons or spirits that are awakened by Naruto's new powers and they see him as an intruder in their realm, so they become antagonists as well. They would use their own dark magic and powers to oppose Naruto.
There could be internal antagonists within Naruto's own village. Some of the more conservative ninja in the village might not trust Naruto's new - found skills and powers obtained from Zetsu. They could try to undermine Naruto or even attempt to exile him, fearing that he has been corrupted by Zetsu's teachings.
Naruto's character would likely become more serious and focused. Training with Shisui and the Sharingan would demand a lot of concentration, so he'd have to tone down his wilder side. He might also become more strategic in combat, as the Sharingan gives insights into opponents' moves.
The Akatsuki could still be the main antagonists. Even with Naruto's training by the Kyuubi, they would be after the tailed beasts. Their goals of collecting all the tailed beasts would put them in direct conflict with Naruto. And they have some really powerful members like Pain and Itachi.