One thing is a sprite, another thing is the source image, the CHR. The NES PPU displays 64 sprites every frame. Each sprite can take any tile from the CHR independently. They may repeat as many times as you want. And each sprite can be placed on any coordinate on the screen, and it can receive its own attributes independently from other sprites.
So, to answer your question and fixing it:
"Is it possible to flip a set of NES sprites that are displayed twice?"
You can't display a sprite twice, you're having two sprites that display the same tile from the CHR. And one of them can be flipped while the other isn't, no problem.