In response to the above poster: Iruka doesn't buff the whole team, only Konoha units. So Kakuzu does not get the buff and shield. There are better options.

Sorry in advance for this long answer. I have used BT Rinnesasuke for a while now and I have a lot of opinions on him and how to support him lol. But if you read it all it will be helpful.

First of all OP, when you say you're thinking of Madara, which one do you mean? Founder Madara and GNW Madara go well with Rinnesasuke but Edo Release Madara, not so much. Sasuke and Kakuzu rely on chakra and Edo Madara's barrier prevents you from getting chakra. So I would not suggest going for him at all for this team/based on the ninjas you have. The other two are fine.

Right now, you don't have a ton of ninjas you could swap out into this team. But I don't think you should take out Kakuzu, you should take out Summer Kakashi and replace him. Kakashi does give that attack buff round 2 but if you are not consistently faster than your opponents it's not worth it in a team like this. Rinnesasuke is not the most tanky ninja and considering some of the most common ninjas right now (Edo Minato, SOSP, Kakuzu) deal wind damage, which Sasuke is weak to, having Kakashi lower his def and res in round 2 means Sasuke may not even survive. And in my opinion, Rinnesas is a ninja you need to survive into round 3 because that's when his mystery starts doing a ton of damage (assuming you have and are using the Y+1 mystery and the +2 scaling passive, which you should be).

Imo, your best option right now is to switch Summer Kakashi with Susano'o Kakashi (and switch to Fire main):

At least Sasuke and Kakashi's mystery will be unmissable. Also I think Fire main is more safe than Lightning. Lightning makes Sasuke immune for 2 rounds but someone like Edo Itachi could just override that I think, and Kurenai, Ibiki, NY Hashirama definitely can. On a Lightning team if they immobile/chaos Sasuke after Kakuzu heals, you can't do anything about it. With Fire main you can set up his shields and negate that (even Edo Itachi, because you will generate 40 chakra before your action). Plus you can get more chakra from the main per round (20 vs 40).

This team doesn't have very long chases/combos but that's because if you do the version with the highest combos, you lose out on Kakashi's chase which causes immobile. See, the combo off Sasuke's mystery in this team looks like this:

And in the "higher number of combos" team it looks like this:

Yeah there are more hits. But Kakashi's chase doesn't trigger (I can't figure out a way to have both a bunch of chases and for it to trigger, I tried with Lightning main too. It's bc it chases knockdown and he's in pos 4, but others who chase knockdown will always chase before him because of position order). In my opinion, that immobile might be more useful than triggering Sasuke's chase twice here (see next paragraph for why). The stats decrease from Sasuke's chase is also nice but idk. You can try both combos. I personally don't like using teams that don't have a chaos/immobile/accupuncture off of the pos 1 mystery's combo but that's just my preference.

You probably already noticed this, but even if you hit an immune ninja who is about to do their mystery with an attack that causes immobile/chaos/acupuncture, it won't actually cause that status to them but it will stop their mystery. This is really valuable imo. It's not gonna work against Minato unless you wait to proc his first universal dodge, because even tho Sasuke's mystery will hit he will dodge the chase. So if you're facing a dodge ninja don't target them. Target the team's most important support or whoever else is mysterying.

That's just a temporary team tho. The best ninja you can get to put in pos 4 in the short term, imo, is BT Chunin Shikamaru. He supports Hidden Jutsu users (Sasuke, Fire main), can decrease Sasuke's cooldown and increase an opponent's cooldown, and he generates chakra. He has a chase that causes immobile but it fits in much better with a longer combo sequence. The team is like this:

But you do want to have his BT. Top priority are his passive (+2 or Y+2, your choice), mystery (Y+1), and his first chase, the flame one (Y).

In the long term, you can work on getting GNW Madara and Edo Nagato. They work well with Rinnesasuke too.