The status of beef and chicken in this regard is the same as that of milk. If the animal was slaughtered before Pesaĥ, there is no halakhic problem, even if it had eaten ĥametz. However, since the stomach may contain undigested leavened barley grains, its contents must be thrown out. If a gentile’s animal was fed ĥametz and slaughtered during Pesaĥ, some poskim forbid consuming its meat, while others are lenient. It is proper to be stringent and not buy the meat of a Jew’s animal that was fed ĥametz on Pesaĥ.
In actuality, most meat is sold in packages, which thus must be labeled kosher for Pesaĥ. Even if the animal was slaughtered before Pesaĥ, when there is no problem if it was fed ĥametz, supervision is nevertheless required to ensure that no ĥametz fell into the meat between the slaughtering and the packaging.
The same applies to eggs: as long as the eggs were bought before Pesaĥ, they are entirely kosher for Pesaĥ; that the hens were fed ĥametz makes no difference because it was not prohibited when eaten. The halakhic status of an egg that comes from a hen that ate ĥametz on Pesaĥ depends who the owner is. If the hen belongs to a gentile, the poskim disagree about the permissibility of the eggs. If the hen belongs to a Jew, even though some poskim are lenient, it is proper to be stringent and refrain from buying such eggs. In practice, there is no supervision on eggs laid during Pesaĥ, so it is best to buy eggs laid before Pesaĥ.
Another problem that has arisen pertains to the markings stamped on each egg. There was some concern that these markings contain ĥametz and that a drop of it might fall into Pesaĥ food. However, I heard from Tnuva’s R. Ze’ev Weitman that all eggs brought to market via Israel’s Egg Production Council (which does not include the black market) are marked before Pesaĥ with a stamp that contains no ĥametz (the relevant mark is a series of stars).