I have no idea how many characters are involved, but assuming there were 4 female and 4 male characters in gen-1, and that no new characters were mixed in, then each person in gen-2 has two gen-1 ancestors, Gen-3 people will have 4 gen-1 ancestors, and gen-4 would have all 8 gen-1 ancestors. At that point any further generations require inbreeding.
It works out that if you have 2n unrelated characters originally, they can breed together for n more generations before inbreeding must start. If n is fractional, you round down: for example, if you have 6 initial characters (n < 3), then you can say that one couple had 2 kids, the other couples has 1 kid each. Then, the siblings marry the two only-children, but you now have a problem, since everyone's already related when you try and come up with some couples for the next generation. So, with 4 or 6 original characters you can only get 2 additional generations.
I could go into more details if I actually cared to know anything about the Naruto franchise ... which I do not care to find out. Believe It!
EDIT: However, the math also works out that for 2n people you can also control how closely the inbreeding must be. For example, 2 progenitors means your kids must marry a sibling (sometimes refered to as a 0th cousin), 4 progenitors mean your kids's kids must marry a first-cousin (e.g. 2 brothers marry 2 sisters in the second generation, to create a third generation who are first cousins), and I'm pretty sure the pattern continues, so if you have 16 progenitors (2^4), then you can wrangle it so that down the track you're not marrying closer than a third cousin, by generation 5.