Why does cooked chicken taste different after a few days in the fridge?
There are a few reasons why leftovers taste different. Here I will base my answer from the chapter on meat of On Food and Cooking by Harold McGee (Which I highly recommend to anyone wanting to learn the whys of cooking). 


  At the same time that cooking develops the characteristic flavors of meat, it also promotes chemical changes that lead to characteristic, stale, cardboard-like “warmed-over flavors” when the meat is stored and reheated.


The reason this is observed in chicken earlier than with pork or beef is the following:


  The principal source of off-flavors is unsaturated factty acids, which are damaged by oxygen and iron from myoglobin,
  Meats with a greater proportion of unsaturated fat in their fat tissue (poultry and pork) are more susceptible to warmed-over flavor than beef and lamb.


Here are a few ways described in the book to minimize the development of off-flavors:


Season the food with herbs and spices that contain antioxidant compounds.
Use low-permeability plastic wraps to cover the meat, and eliminate air pockets in the package.
Reheat the meat properly.
Of course, eat as soon as possible.