Naruto might become more competitive. For example, if he sees Hinata spending time with someone else, he'll try to outdo that person in various tasks, like training or helping villagers. He could also get moody and a bit withdrawn, not his usual energetic self. It's his way of dealing with the unfamiliar feeling of jealousy.
Naruto could start to act impulsively. He might interrupt Hinata and the person she's with, making up excuses like he needs Hinata's help with something urgent. He'll also probably try to show off more around Hinata. He'll do his most powerful jutsus in front of her, hoping to get her attention back on him. And he'll be constantly looking at Hinata when she's with the other person, with a scowl on his face.
In some fanfictions, Naruto is completely oblivious at first. He doesn't understand why Hinata is acting strange. He just goes about his day, being friendly as usual. But as Hinata's jealousy becomes more obvious, he might start to notice that something is wrong. He could be confused and try to ask Hinata what's bothering her.
Naruto would probably be extremely hurt. He has always considered Hinata a friend and perhaps more. Betrayal from her would be a huge blow to his trusting nature. He might initially be in denial, not wanting to believe that Hinata could do such a thing.
Hinata might be very hurt. She's a sensitive person, so Naruto yelling at her could make her feel small and sad. She might start to doubt herself and her abilities.
Hinata would be overjoyed. She has loved Naruto for a long time, so his proposal would be like a dream come true for her. She might start crying tears of happiness and immediately say yes without hesitation.
In a fanfiction scenario, Naruto being a jealous husband might lead to some internal conflict. He has always been confident, but when it comes to Hinata's affection, he might worry that he's not doing enough. So, when he sees Hinata having a normal conversation with someone else, he might start to doubt himself. This self - doubt can be explored in the story, and through his relationship with Hinata, he can learn to overcome it.
One common theme is Hinata's struggle with her self - esteem. When she gets jealous, it often stems from her feeling that she's not good enough for Naruto compared to other girls. For example, in many fics, she sees Naruto being close to Sakura, who is more outspoken, and Hinata feels inferior.
Naruto might be shocked at first. He could stand there frozen, unable to believe what he's seeing. His face would probably show a mix of confusion and hurt.
Naruto would be extremely hurt. He loves Hinata deeply and to find out she cheated with Kiba would be a huge blow to him. He might go into a state of shock and disbelief at first.
He could also become very sad and withdrawn. Naruto has always valued his relationships, and losing Hinata's love would be a huge blow to him. He might start to question himself and wonder what he did wrong.
He might become really withdrawn. Naruto is a very emotional person, so if Hinata breaks his heart, he could isolate himself from his friends and the village. He would probably be too hurt to face them.