Love and relationships are very common. Since it's related to 'Days of Hana Kiss', the development of the romantic relationship between characters is often explored. Another theme could be friendship, as the characters' friendships can play an important role in the story.
You can try searching on fanfiction platforms like Archive of Our Own (AO3). It has a large collection of fanfictions from various fandoms, including 'Days of Hana Kiss'. Another option is FanFiction.net, but the quality may vary more there.
It's also possible that Hana is related to one of Naruto's friends. Maybe she's Kiba's sister or something. And because of her connection to Naruto's friend, Naruto feels responsible for her safety. So when she's in trouble, Naruto steps in to save her without hesitation.
Hana could be an original character created for this fanfiction. Maybe she is a new ninja in the village who Naruto falls for, but she has a hidden agenda that ends up breaking his heart.
To create an engaging Naruto and Hana Hana no Mi fanfiction, start with a strong concept. You could combine a mission in Naruto with the powers of the Hana Hana no Mi. Let's say Naruto and his team have to rescue a hostage, and a new character with the Hana Hana no Mi powers joins them. This character can use their powers to create distractions during the mission, like growing large flower structures to block the enemy's view. Another important aspect is the interaction between the Naruto characters and the new element of the Hana Hana no Mi. Their reactions and how they adapt to this new power can add depth to the story.
A great plot idea for this fanfiction is a time - travel scenario. A character from the future, who has mastered the Hana Hana no Mi, travels back to the Naruto era. This character could use their powers to change the course of history, for better or for worse. Maybe they try to prevent a major war by using their flower - based powers to heal relationships between different clans. Or, there could be a plot where a group of ninja are sent on a quest to find the origin of the Hana Hana no Mi in the Naruto world, believing it holds the key to a great power that can save their village from an impending doom.
Their relationship could develop slowly. At first, it might be awkward as they are strangers in a way. But Naruto's friendly nature could break the ice. He might share stories about his adventures, which would intrigue Hana. Hana, in turn, could show Naruto the traditions of the Inuzuka clan. They would gradually become friends and then, as they see each other's good qualities more often, fall in love.
In a fanfiction, Naruto could befriend Hana and Tsume in a different context than in the original series. For example, they might meet during a training session in a hidden forest. Their different personalities would create interesting dynamics. Naruto's optimism, Hana's calmness, and Tsume's intensity would all play a role in how they interact.