At first I couldn't put my finger on it, but I actually watched the two vents when I turned on the air, flies come out and they are large in size and they are loud. This is nasty, In addition I notice a fowl odor when air is turned on. Who should I call a plumber and pest control?

Most Pest Control companies do not remove animal carcases, your best bet is to call a plumber with one of those wire cameras to snake through your vents. Locate the carcass and remove it yourself.