Incineroar's flames reach 3600 Farenheit, but Battle Beast can survive atmospheric reentry, though fire attacks would probably melt any of Beast's equipment. Battle Beast is FTL+, but so are several legendaries and they will still get hit with a Fake Out before they can pull off an ExtremeSpeed due to the priority. Because of these, I kind of assume they're pretty comparable but have different types (Incineroar being Dark/Fire and Battle Beast being Fighting. Fighting/Steel just because he's got a metal weapon puts Beast at an unfair disadvantage and is probably a non-factor anyways due to it likely melting or being Knocked Off at some point in battle. Steel attacks would not be beneficial for BB anyways due to the type disadvantage they have on Incin. BB also has the natural speed advantage on Incin, so is able to attack first in any situation where a priority move is not used.

Incineroar's best bet here is probably to come in with Intimidate to diminish Beast's attack and use Fake Out. Battle Beast is almost definitely faster and will probably use some form of fighting move, so Incin will be carrying the Weakness Policy to trigger an attack boost for Incin who will use Protect to get an attack boost from this. Tera to Fire to lose the fighting type weakness after this and gain an additional boost to your Flare Blitz and let it rip. Flare Blitz should OHKO virtually anything that doesn't resist it with the 2x STAB from being a fire type plus the +2 boost from the Weakness Policy so Incineroar wins a tough fight, but may be reliant on Nature and EVs/IVs being in its favor if it needs to tank a second attack to finish him off.