This seems to be more like the "Batman: The Brave and the Bold" cartoon of comic books. Just more light-hearted and the action moves around a lot bouncing off one guest star after another.
of the silver age heroes, hal and barry have the most timeless costume i think. then ray.
There's a red line that is his mouth, but I think it's just the same brown line used for his body outline. It may be a bit redder to show that it's a lip or it looks a bit redder because it's surrounded by his skin color.
The eye shadow is the black line between his eyes and mask, which could be one since, if you remember the 90s Batman movies they have to put black eye shadows around the actor's eyes when wearing a mask so you can't see their skin but they can still see easily from the mask.