How do I repair a nick in vinyl floor?
Option 1: Try some nail polish of an appropriate colour.  It's not a perfect fix by any means, but it is cheap, and you are replacing soon.  

Option 2: Cut out the entire 'tile' on the 'grout' lines and cut a matching piece from leftovers if you have any. Glue it down with contact cement. The edge of the patch will collect dirt and become ugly pretty fast.  I don't recommend this if it's in the center of the field.  It's ok for edge work.

Option 3:  Put a rug over it.