I think the do and do nots are, do it atractive and usable, and do not make it unatractive and usless.
In my opinion you have it easy.
Greek clasic decoration on vases for example have a timeless style. It is abstract, it is well defined, it is... flat! you can adapt it quite well. Greek vase
Here is the adaptation that Disney made for the Hercules movie
And thinking about this... what would be wrong about using skeuomorphism?
Probably your app main interfase could be Greek reliefs.
Greek reliefs They are "flat" in escence. They could be easily adapted into a flatter version.
There is a trend in flat design. A shadowed flat design:
Flat Design with Shadows
Google's Material design is also a shadowed version of the flat design.
There are some examples of texture on flat design using noise.
Maybe it is time we start using a flat textured flat design trend. Actually I will start doing it now! Remember the day a new trend started!
In my opinion we are using Greek design basis all the time.