Ok, I think I deduced a way Marvel lawyers can have the rights to Kang:
Fox owns the time-traveller Nathaniel Richards who also can go by the alternate identities Rama-Tut, Scarlet Centurion, and Immortus
Marvel owns the time-traveller Kang the Conqueror (since he apparently he didn't first take the name of Kang until he was introduced in The Avengers) and all additional identities.
Maybe they share some identities but I think there is definitely a way they can sort of split the the character cleanly into what applies to the Fantastic Four and what applies to the Avengers, especially since with Kang there are a numerous number of alternate timelines with alternate timeline versions of Kang.
The precedent for a split like this in the films is Viper/Dr. Green in The Wolverine (with her toxins and ties to Silver Samurai) whose counterpart in the MCU is Ophelia/Madame Hydra in Agents of SHIELD with the Hydra ties. They mostly handled that by cleanly drawing a line through aspects of the character and simply not referring to the aspects their universe doesn't "own".
Also, we've seen how certain rights are delineated such as Marvel having rights to The Watchers as a race (or at least they share them) but don't have the right to Uatu (who is linked the the Fantastic Four) or how Marvel has rights to the Skrull and even can use Super-Skrull (from what I've heard in the past and that seems to be true from the concept art for Captain Marvel) but they don't have the right to The Super-Skrull, Kl'rt.