There is a lot of critique of Black Adam, so I don't want to add my voice to the people who are criticising it. Even the Critical Drinker's review focuses on pointing out the flaws in the movie (as well as the pros) but doesn't offer suggestions to make it better.

What I'll try to do is suggest some changes, which have the potential of making the story a lot better (IMO).

Theme

I like to start with the theme of the movie. What's Black Adam's theme? What is the movie trying to discuss?

Let's take one of the scenes from the movie, where BA faces off with Hawk Man (HM). HM tells BA, "Heroes don't kill people", and BA responds "Well I do."

In multiple different places they talk about what's right and what's wrong. Heroes and Villains. It's easy to tell who's bad and who's good when you're the one drawing lines. When you've seen so many futures as I have you cease to believe in absolutes.

One of the biggest BA marketing push is BA's version of justice. He's bad ass. He kills people.

Based on all this, I think a good theme would be: "Justice is not black and white"

The movie would then examine the concepts of Justice, due process and when is it okay to bypass due process for the greater good.

This can be done by creating a contrast between HM and BA, since both of them embody the different ideologies.

What would make the movie good IMHO is if we never really come to a solid answer, rather show how both approaches have significant flaws.

If you wait for due process, you end up with injustice prevailing and people suffering. 

If you shortcut and "kill them all, and let God sort them out", then you end up hurting people who don't deserve it.

This conflict would be best embodied by having a Reluctant Judas character. Let's see how we can do that by examining the characters in the movie, and assigning each one a script role.

Characters

Black Adam

He embodies the alternative view on justice. In order to help people you have to have some darkness in you. Sometimes you have to make the unpopular choices.

Hawk Man

He embodies the Idealistic super hero. The one whose goal is to keep the peace; to maintain due process; to ensure traditional justice is carried out.

Dr. Fate

He's the mentor. The rock, no pun intended, in which the other characters find comfort and strength. 

Adriana and Son

I'm going to ignore the son character, because he serves the same thematic purpose as Adraina. The only thing he adds is a connection between BA's past and the present. He serves as a reminder to BA of his own son. Although this doesn't come out very well in the script.

Adriana represents the oppressed people, who suffered at the hands of the Villains, Intergang. She wants justice, but lacks the power and resources to actually make it happen

Ishmael

He represents the evil in man. Him and Intergang serve the same purpose. They oppress the of the people of Kahndaq; mistreat them; and take away their freedom.

I think I'm going to stop here, as these characters are the only ones necessary to drive the plot forward in its bare essence.

As you can see what is missing is a character which can bring forth the theme of the movie such that we do a lot more showing and a lot less telling. 

Unfortunately, the theme primarily comes out via dialogue. Adriana admonishes the Justice Society for not caring about the injustice taking place in Kahndaq. She poses the question: what should Justice should look like? Should it be dark and swift, as what BA does, or should it be methodical and by the book as what HM does.

What we need is a way to show these two opposing points of view, rather than just tell the audience about them.

What we need is a Reluctant Judas

Reluctant Judas (RJ) and the Theme

I would cut out or reduce greatly the role of Adriana's son. Make him be part of the comic relief and leave it at that. Add the RJ character, who starts off helping Adriana out with her quest, but at the same time, he's feeding intel to Ishamel.

Ishmael would be more of a background character, who is directing Intergang from behind the scenes.

We could build up a relationship between RJ and Adriana, thereby making his betrayal all the much worse.

RJ is not blind to the injustice in Kahndaq, but he has lost too much, and just wants a better life for himself, even if it comes at the expense of his nation. Something, which Ishmael promised him, if he gets him the crown.

In RJ's journey we can see how he's both bad and good. He cares for Adriana, but at the same time he can't waste the opportunity for a better life.

RJ's demise would come in the middle of the movie. When things go side ways he facilitates the kidnapping of Andriana's son's. In retaliation, BA extracts the information he needs from him and kills him in front of Adriana and against her wishes.

This simple act of killing someone Adriana cares for, even though RJ has "sinned" against her, will really bring out BA's dark justice. And will make Adriana fear him, more than like him. She knows that she needs him to save her son, but at the same time fears his unpredictable violent nature.

BA killing RJ will be a precursor to him almost killing Adriana's son by mistake, and therefore, making his decision to give up his power a lot more impactful.

The addition of the RJ character will also focus the script. 

We're not going to have to waste time with Adriana's son. You can still keep all the jokes, but cut out the rest. The boy can still serve as a reminder of Black Adam's son. But this will manifest itself through BA's interaction with Adriana, rather than with the son.

We would build up a friendship between Adriana and BA. This friendship can be used as a vehicle to bring out the hurt and the guilt BA feels. This friendship story-line would culminate at the movie's mid-point when Adriana's son gets kidnapped, and BA kills RJ after he gets the information he needs.

Through the Ishamel/RJ interaction we could better understand the motivation and politics of Intergang.

I would also cut down the time spent with the younger members of the the JSA. In fact I would cut out the wind girl completely. And keep Atom Smasher for his comic relief .

Then I would use the time saved there to delve more into the Adriana/BA relationship and the Ishmael/RJ interactions. Flesh out the RJ character and make the audience empathise with his motivation. The audience won't agree with him, but at the same time, they wouldn't want to see him die. And when BA kills him, it also makes the Audience both like and fear Black Adam for the same reason as Adriana. His actions are unpredictable.

The rest of the action and main elements in the story can stay the same.

Anywho, that's all from me. Over and Out.