One way is through brute force. Houndoom could be extremely powerful in the fanfiction and simply overpower Naruto's attackers. For instance, if there are some assassins after Naruto, Houndoom could charge at them and knock them out with its physical strength.
Another possibility is that Houndoom has some sort of healing or protective magic in the fanfiction. So when Naruto is injured, Houndoom can use this magic to heal him or create a protective shield around him to keep him safe from further harm.
Houndoom might also work together with Naruto's friends in the fanfiction. For example, if Naruto is captured, Houndoom could team up with Sasuke or Sakura. Houndoom uses its unique skills like tracking by smell to find where Naruto is held, and then they all work together to rescue Naruto from the captors.
In some Naruto fanfictions, Houndoom might save Naruto by using its powerful fire - based attacks to fend off enemies. For example, if Naruto is surrounded by a group of rogue ninjas, Houndoom could blast them with its Flamethrower move, creating a wall of fire that the enemies can't cross, thus buying Naruto time to escape or come up with a counter - attack strategy.
Fu could use her healing abilities. If Sakura is attacking Naruto with some kind of harmful jutsu that causes internal damage, Fu can use her healing powers to counteract the effects. She could also transfer some of her own life force or energy to Naruto to keep him alive and stable while dealing with Sakura. This would be a more spiritual or mystical way of saving Naruto.
One way could be that Naruto uses his Sage Mode. In this mode, his senses are heightened, allowing him to easily detect the location of Moegei and the kidnappers. He can then quickly move to the scene and overpower the kidnappers with his enhanced strength and speed.
One way is that he could use his super - senses to detect any flaws in the fanfiction's plot. Then, he can somehow communicate with the writer (maybe in a magical way) to suggest improvements. For instance, if there's a lack of action in the story, he can inspire the writer to add some of his signature acrobatic fight scenes.
One possible reason could be Naruto's natural sense of justice. He can't stand to see a child in danger, and Koyuki being a child at that time, Naruto's heroic nature kicks in. He has always been the type to help those in need.
One way is by using his Sage Mode. Naruto in Sage Mode has enhanced senses and chakra control. He could use these advantages to refine the Hiraishin. For example, he might be able to make more precise teleportations or detect potential threats at the destination of the Hiraishin more accurately.
In some fanfictions, Naruto could gain the ability to fly as a result of a forbidden jutsu. This jutsu might be so powerful that it not only gives him flight but also enhances his other abilities. For instance, he could be forced to use this jutsu in a life - or - death situation against a very powerful enemy. Also, he could fly if he absorbs some kind of special energy or power - up from an ancient relic. This power - up could transform his body in a way that allows him to fly, like growing wings made of pure chakra.
One way could be through adventuring and finding rare treasures that can be sold for a high price. For example, slaying a powerful monster and selling its parts.
Maybe Absol has a special power that it doesn't fully understand, and Houndoom, being more in tune with the darker aspects of the Pokemon world, helps Absol to control and master this power. Along the way, they form a deep bond and face various challenges together, such as natural disasters in the Pokemon world that are affecting their habitats and the other Pokemon around them.
A possible plot could be that Absol and Houndoom are from different packs or groups in the Pokémon world. They meet by chance during a natural disaster, like a forest fire. They have to work together to survive and in the process, they develop a bond that turns into a mating relationship.