Luffy's character would develop in several ways. With the Flame - Flame Fruit, he'd have to learn to control the fire element. This would require discipline, which is something he doesn't have much of in the beginning. As he masters the power, he'd grow more responsible. Also, his reputation among other pirates and in the world would change. He'd be seen as an even more dangerous and unpredictable foe, which would add to his allure as a pirate captain.
If Luffy ate the Flame - Flame Fruit in fanfiction, his character development would be significant. Firstly, he'd need to adapt to this new power. Fire is very different from his stretchy abilities. This adaptation process would make him more patient as he figures out how to use it effectively. His relationships with his crew might also change. They would see him in a new light, with this powerful and potentially dangerous ability. He might become more protective of them, knowing that his new powers could draw more dangerous enemies. And in the face of new challenges that come with the Flame - Flame Fruit powers, Luffy would likely become more strategic, thinking ahead to how he can use his fire abilities in different situations.