Flying Rats are 200 collectible pigeons located all around Liberty City in GTA IV which Niko must find and shoot (or blow up). The pigeons are generally found in out-of-the-way areas, but can be easily noticed by the distinctive cooing sound they make and the red glow they're highlighted with. Killing all 200 Flying Rats adds 2.5% to the Game Completed Percentage and also unlocks an Annihilator helicopter on a helipad near Star Junction in Algonquin.
These pictures below from whattheydonotwantyoutoknow.com are helpful, but I found this real life website to be much more helpful. It's called gta4onlineguide.com It has pictures and descriptions for each flying rat, a picture of Niko with the rat, and a zoomed in and zoomed out picture of the pause menu map pinpointing the rat's location. Awesome! Check it out:
The in game website whattheydonotwantyoutoknow.com shows the location of the flying rats. Small dots are one flying rat, while large dots represent two.
On Happiness Island, the large dot represents five flying rats.
One Flying Rat is not represented on the whattheydonotwantyoutoknow.com website. This one is located on the far west/south-west side of the far left island (Alderney), on a construction site.