Black Adam is the main nemesis of Captain Marvel in the comics, but it's said that he won't be appearing in Shazam! at all, opting for his own solo movie. While the film still looks to be in early stages of development, we have a bit of news on what the story is based on plus which other characters could appear.
According to Discussing Film, Black Adam is said to be based on the Dark Age comic and will feature the likes of Stargirl and Atom Smasher. It's also said that Hawkman will be the main antagonist of the movie. The Dark Age comic line basically had Adam stripped of his powers and he goes on a journey to regain them as well as resurrect his dead wife.
While Dark Age takes place in the contemporary comic timeline, I have a feeling they're going to make the movie a period film—sometime around the rise of the Egyptian civilization. Hawkman has deep roots with that culture, and it would make sense seeing that Adam turned himself into a conqueror after he gained the powers of Shazam.
Then again, this is just my guess based on a rumor. Until DC announces anything official, all the fans can really do is guess.
Hopefully, there's a small tease for Adam somewhere in Shazam!. After all, he was the last holder of the powers before they were transferred to Billy Batson. I'm just hoping hey culminate this all into the Shazam family taking Adam on.
Black Adam is said to be aiming for a production start in March 2020. With that in mind, we could be looking at a 2022 release.