Has the reincarnation of Indra and Ashura ended, after Naruto and Sasuke fight? Or will there be new reincarnation of them again, looking for new hosts ?
According to Naruto wikia:
The reincarnation cycle will not start again until both of the current reincarnations have passed away; the brothers would not reincarnate until Madara's death, which would occur decades after Hashirama's.
Also on top of the page, it says: Naruto Uzumaki, the current reincarnation of Asura.
The only thing that differs with Naruto and Sasuke was that they didn't have the same conclusion, as the previous reincarnations:
Ultimately, Naruto managed to accomplish what all of the previous reincarnations had failed to do: end the rift between the two lines of the reincarnated brothers. Naruto achieved this after defeating Sasuke, who finally accepted Naruto's ideals at the end of their fight. This brought about the end of the bitter feud that had lasted for centuries. According to Black Zetsu, the reincarnations of Indra and Asura were almost always in conflict with each other and rarely worked together. Naruto and Sasuke are one of the exceptions, assuming other exceptions have existed throughout the centuries.
This question is hard to answer with certainty.
Based on Naruto's words before the final fight with Sasuke, the feud would end after that battle. (Chapter 692, pg 17)
Sasuke then claims the "eternal destiny the sage of six paths talked about [would] end" if he dies. Sasuke didn't die, so the "destiny" (reincarnation cycle) may still be alive. http://narutobase.net/manga/Naruto/698/18/
Or maybe Naruto ended it by forcing Sasuke to admit defeat, something the other reincarnates of Indra never did.
Based on what happened when Obito died, there is a soul and afterlife of some sort, so one could argue that, with the "feud" over, there is no need for them to reincarnate again, and they could finally pass on to that afterlife.
(Chapter 688, page 6)
In conclusion, I don't think there is a definite answer. You just have to choose what to think yourself on this one.
(Chapters and page numbers from narutobase)
I would argue that the reincarnations end with Naruto and Sasuke. Indora and Ashura reincarnated probably because they still hadn't ended their feud. Because Naruto was able to end the brother's feud, that probably also ended the cycle of reincarnations. In other words, the brothers made up through their reincarnations (Naruto and Sasuke), so they have no reason to keep reincarnating again.
I'm not predicting or giving a direct answer to the above question, but I say that the reincarnation can take place again not for the sake of any dispute between brothers like before, but for the extension of the family tree or expansion of clan and lineage...it could be now a reincarnation of brothers for the sake of watching over the true will of their dad...and also to innovate a new era with cooperation after long strife...
besides, in resolving to do dad's will from now on, madara will be free from zetsu's deceipt and darkness will not be the way out for the sharingan but Hagoromo's full powers might certainly enhance the sharingan or again, honest cooperation between the brothers can make things to run smoothly (like hashirama cells, tailed beasts' chakra ,hagoromo's legacy, etc)
therefore since there are various clans, the two bothers can incarnate as clan leaders (madara, hashirama)...and a new story emerges with their collaboration...and i think that there are still some boss battles...kaguya mentioned that she was pursued by some three violent persons and that she escaped to the ninja world where she arrived already fierce and powerful...this therefore means that madara's story of which he was convinced about kaguya eating a fruit and thus possessing chakra was wrong!?!
i think the reincarnation is possible and can be appropriate in a collaboration context...thus madara indora can be appreciated, cheered and thanked for the incarnation idea...i don't know if it will bore or it will still be interesting and have some sense (because previous boss is now walking with actor, what next?)
to be honest, if naruto and sasuke incarnates are in collaboration, with their actual power levels (ten tails and rinnegan), i don't imagine a threatening boss battle against them...even if they possess the power level below the above mentioned power level, if incarnates of madara sasuke and naruto are in collab, i still think that boss battle has been cleared in advance
The reincarnation cycle definitely ended because indra said a purpose to his reincarnation and ashura said he will also reincarnate as to stop him. Every reincarnates failed in their purpose, but with naruto and sasuke, naruto fulfilled ashura's and hagoromo's wish(indra and ashura working together in full harmony without hatred, but only with love and brotherhood). Sasuke overcame his hatred and 100% doesn't wish to do what indra wished to do, in other words, indra overcame his hatred, and ashura succeeded in helping indra overcoming his hatred. And thus the cycle of hatred also ended. So there is no reason to reincarnate anymore.
All the other indra reincarnates before sasuke doesn't agree with ashura's ideologiea, and dies while holding onto indra's ideologies leaving behind a purpose for reincarnation. That definitely ended with naru-sasu in their last battle.