If you play the flute and want to learn a second instrument, you should learn piccolo! The two instruments are relatively similar, so you can get started easily. However, you may need to work on your embouchure when you first start. The piccolo is smaller, so you'll have to consider that when playing it.
How hard is it to learn the piccolo?
During my college days, I picked up the flute quite quickly, but I had a difficult time achieving a good tone on the piccolo. That said, it would not be impossible to learn on its own, just more difficult. You can find cheap flutes at pawnshops or on craigslist. You may try picking up a cheap one to begin on.
Should I learn flute or piccolo?
While flute and piccolo can be played fairly interchangeably, it's generally best to start with the flute. This will give you a great foundation to work from and will help you build endurance as you learn a broad range of notes and hone your technique.