Assuming people (as opposed to dogs, cats, garbage cans etc.) ate all these chickens, this works out to: 1743 chickens per lifetime.
Similarly the reported 208,511,114 turkeys in 2013 corresponds to: 52 turkeys per lifetime
The reported 97,203,867 pigs in 2013 corresponds to: 24 pigs per lifetime
The reported 34,799,542 cows/calves/cattle corresponds to: 9 "cows" per lifetime
The reported 4,816,359 sheep in 2013 corresponds to: 1.2 sheep per lifetime
USA Today is wrong by a factor of 25 for sheep, and is a little high for the other land animals. Also, USA Today leaves out ducks (24,575,000 in 2013) which correspond to 6 per lifetime.
Additionally, the "How many animals does a vegetarian save?" calculates 148.96 fish including shell fish consumed per person in 2013 in the USA. This is overwhelmingly due to shrimp (126.42), with scallops (4.72) being a distant second.
Issue: Does the average American eat 7,000 animals during his/her lifetime?
2008 figures give a average number of total animals consumed per American lifetime as 21,000 (sea animals-19,000 and land animals-2261).
2009 figures give a average number of total animals consumed per American lifetime as 15,000 (sea animals-13,000 and land animals-2159).
2011 figures give a average number of total animals consumed per American lifetime as 16,000 (sea animals-14,000 and land animals-2113).
The average American might eat more than 7000 animals based on the quoted statistics from the above sources which are clearly noted not to be entirely accurate and similar to the OP's source. The numbers tend to vary on the higher side when combined with the exports and independent rounding mentioned by the source from United Poultry Concern.
In 2012, the average American consumed 71.2 pounds of red meat (beef, veal, pork, and lamb) and 54.1 pounds of poultry (chicken and turkey), according to the U.S. Department of Agriculture. The average amount is likely a bit higher.
Also there are no real statistics on number of finfish or shellfish killed and the numbers provided are all based on best guesses and estimates based on total weights and extrapolation.
The corresponding per capita consumption figures for Oceania, North America, Europe, Central America and the Caribbean, and South America were 24.5, 24.1, 20.8, 9.5 and 8.4 kg, respectively.
Meat consumption is seen to rise in the U.S and EU over the past decade and the United States is noted to have a meat consumption at more than three times the global average.
Overall meat consumption has continued to rise in the U.S., European Union, and developed world. Despite a shift toward higher poultry consumption, red meat still represents the largest proportion of meat consumed in the U.S (58%). Twenty-two percent of the meat consumed in the U.S. is processed. According to NHANES 2003–2004, total meat intake averaged 128 g/day. The type and quantities of meat reported varied by education, race, age, and gender.
The U.S. also exports beef, pork and poultry apart from its own consumption at a higher rate when compared to other countries in the world.
Exports in 2010 accounted for 18.9 percent of U.S. pork production, 19.8 percent of poultry production and 9 percent of beef production.