Continuity mistake: When Barry is looking at the gun case in the Batcave, a cork board is visible in the background covered in raggedy playing cards. The one to the left of the center Joker card has blood on it, a lot of it around the bottom right corner of it. Later when Batman looks at the cards, the blood on that card is significantly less. There is also a card to the right of the Joker card that is torn with no blood on it. But in the close up when Batman is looking at it, that card now has a large blood spot in the center. The card symbols on the cards are also closer together, the cards above the Joker are significantly less damaged, and change from suit of hearts to a different suit. The entire board seems different. A few shots later, the cards above the Joker card are back to hearts again. (00:20:45 - 00:25:30)
Chosen answer: Despite the ending in Flashpoint to indicate a Darkseid invasion, War is not a sequel. It's a reboot. While both films were part of the DC Universe Animated Original Movies series, War is the first movie of the series that is now part of the DC Animated Movie Universe. This is also why the voice actors are different.
Bishop73