The inking does a lot of heavy lifting in those styles! As long as it looks interesting as just lineart, it'll look interesting with flat color, too. It speaks to how well the characters are designed as well.
If you feel like your art is missing something without shadows, try putting in more lines for folds, hair texture, etc. You may also just have to work more on your stylization!
It's totally an option to skip shading or even be a little messy. You need to prioritize speed and not burning out when it comes to comics. 
Here's an example of some of my work with flat color. The only "shading" I did was during the ink stage, I used black to shade under their chins and the really dark colors, then put a basic highlight on them. No other rendering beyond that, and a lot of people have said that they didn't notice it was largely just flat color until I pointed it out! Definitely made this go faster than if I had fully colored every single character.
The inks: