Polite Patamon gave a good answer, but I thought that I'd elaborate more.
The answer to your question is Yes, there have been various occasions in the Anime where characters have eaten Meat, or at least referenced to it.
Meat is often shown in the anime, but while it has never been directly shown to come from Pokémon, no other food source has yet been explained.
An example is in Go West, Young Meowth where in one of the flashbacks, Meowth is shown eating Chicken. Another one in To Master the Onix-expected has an old lady mentioning Muskrat Meatballs (For Reference a Muskrat is a type of animal).
If they do eat meat, it means that they are eating thier supposed partners. Kind of same for all the Pokemon apart from heatmor(who eats Durant).
That second part however, is partially flawed. Why you ask?
Animals have been shown throughout the anime (actual animals), and many references to them have been made in regards to food. So you cannot rule out the possiblity of food coming from those. :D
Beauty and the Beach
Brock attempts to attract customers to a restaurant by advertising unusual animal-themed dishes, including french-fried flounder, seven-layered crab cakes, squid on a stick, and clam juice snowcones.
The Battling Eevee Brothers
In one scene, James is holding a lobster.
Riddle Me This
While Ash and his friends are looking for a hotel to stay in, a picture of a tiger can be seen in one of the hotels. Furthermore, during Gary's banquet, a fish is seen sliced up.
Go West, Young Meowth
While Meowth was looking for food, he came across some fish bones. Meowth is also seen eating fried chicken.
Bulbapedia also says;
Animals have been seen in the anime.
However it is true that they also may be getting food from Pokemon.
However, it has been mentioned that some Pokémon are hunted and used for their meat: Farfetch'd in particular are noted for making a good meal, especially when cooked with leek, and were nearly hunted to extinction because of this, ultimately leading to their rareness.
During a story arc within the Gen II games and their remakes, the newly reformed Team Rocket begin stealing Slowpoke, cutting off their tails and then selling them as a rare delicacy. It is indicated that the tail is not eaten, but is sucked or lightly chewed on; similar to the manner in which a person would enjoy Honeysuckle.