Trinity War has lots of Soldiers. You almost need a score card to determine who is on what side.
Lets exam the forces.
Justice League of America
Justice League Dark
Shazam or Black Adam. I only know one thing from the images so far, he is not a member of Justice League dark. He is fighting Deadman in the first gatefold DC gave us.
Doctor Light. Again the only thing DC is showing us is that he is fighting a member of Justice League Dark.
The Trinity of Sins.
We still don't know which teams they are linked to.
Phantom Stranger has teamed up with Justice League Dark.
Pandora has been looking to team with Justice League.
The Question is just now showing up in Phantom Strangers book. So therefore it is still up in the air.
My take on the War.
1. The Trinity of Sins is linked to Shazam. We know this because the Wizards who punished the Trinity wore the mark of Shazam.
2. Pandora's Box is the at the center of the conflict. Again we know this from the Free Comic day story and many stories since.
3. The Question holds a grudge against Phantom Stranger. You need go no further than Phantom Stranger's book to know tha.
4. Players like Zatanna will change teams. Johns has just indicated that in interviews with various comic book sites.
5. Change is coming to all the teams. Again John's has said that things will be different.
So there is my take so far. We will find out in July what really happens.
Go Forth and Do Well.