So..... what system? I assume SNES.... but without CX4.
Assuming you're using the "standard" square sprite sizes and not the unofficial rectangular sprite sizes, the concept is the same as it is with 8x8 sprites.
Assuming 8x8 sprites forming a 16x16 image:
Note that you'll actually have to change where the tiles are drawn as well as actually set the 'flip-x' attribute bit.
On SNES, with 16x16 sprites, the above is all done automatically when you flip the sprite. It will flip each 8x8 tile, and also reconfigure their drawing pattern to be mirrored as well. But if you are constructing a larger sprite out of 16x16 sprites, you'll still have to reconfigure those on your own.