Does this black Adam still have invulnerability? The only thing that would affect him is magic.
I've just recently read a large amount of post-crisis comics featuring Black Adam because my interest in him rose a lot thanks to his movie. To my knowledge, he indeed can be affected by non-magical means from opponents at his level in this iteration.
See these examples:
1,
2,
3,
4,
5 (The guy wearing the robot suit, not the girl using a "spirit shot")
With that said, it's much easier said than done to put Adam down in a straightforward beatdown kind of way. He's fought the majority of the JSA on his own without going down for the count, as long his powers work,
on multiple occasions. Albeit, the second time shown they are missing a few notable members, and the third time, its arguable that not all of them are in top shape. Still, this is not to be discredited, even Hawkman with Alan Scott's power added on to his wasn't enough to put Adam down while he's in his transformed state.
He even stood against a much larger group of heroes featuring heavy hitters such as Martian Manhunter, Power Girl, Guy Gardner, John Stewart, Alan Scott, Hawkgirl, Firestorm, Donna Troy and many more all at once, only losing once he was forced out of his transformation and had the word which triggers it changed. (There are two separate depictions of this event, here I will link imgur albums containing both:
1,
2 )
Although it does sound like Danny might have the means to do it.
Danny either goes for physical punches (which won't do anything until his RE buffs him to Black Adams level) and energy blasts which effect the body on a molecular level, the soul, and mind.
I don't know what Black Adam starts with.
Adam starts with straightforward hand to hand combat and sticks with it for the majority of his fights. He excels at these superpowered brawls he engages in, able to take on top dogs like Superman, Captain Marvel, and Martian Manhunter the same way he'd take on someone like Atom Smasher or Wildcat, and able to beat down many opponents all at once.
He fights with an unmatched fierceness among these heroes and
won't hesitate to
take extreme measures in attaining his victory.
He situationally uses his thunderclaps when needed, not shying away from doing so if it can be advantageous for him. Empowering his attacks with electricity or attacking with lightning strikes in any form is a tactic which I found to be surprisingly rare for him in my reading, seemingly only reserved for times when he is really serious.
These energy blasts sound problematic, seeing as Adam doesn't resist two of those three things. His mind might be alright, however, seeing as he was able to ward off
mental control from Martian Manhunter before. Would it be possible for him to
do away with them with a thunderclap?
Having said all this, I am by no means an expert on DC comics, and I could be missing information (although I have read nearly all of the comics Black Adam has listed under his "appearances" in the post-crisis era, on the DC wiki.) Someone else may be able to provide better information than me.