The sign "PINK" is an "initialized" version of the sign RED.
Instead of using an "index finger" or "R" handshape, what you do is use a palm-back "K" handshape and drag the tip of the middle finger down across the lips twice.  You might be asking, "Why a 'K' handshape?"  A "K" handshape is simply an "upright" "P" handshape--and "P" is the first letter in the word pink.

 

Related sign:

The sign for "red" is made by stroking your lips one time with the tip of your index finger.
The sign can also be made by forming the letter "R" with your right hand--but why?  The "index finger" version works just fine and means "red" without needing the more complex "R" handshape.  This is ASL -- not "English on the hands."

Notice in this example how I change the "index" finger into an "x" hand? Or you can just leave it as an index finger.  Either variation is fine.
You will also see this sign done with a double motion.