The status of beef and chicken in this regard is the same as that of milk. If the animal was slaughtered before Pesaḥ, there is no halakhic problem, even if it had eaten ḥametz. However, since the stomach may contain undigested leavened barley grains, its contents must be thrown out. If a gentile’s animal was fed ḥametz and slaughtered during Pesaḥ, some poskim forbid consuming its meat, while others are lenient. One should be stringent and not buy the meat of a Jew’s animal that was fed ḥametz on Pesaḥ.
In actuality, most meat is sold in packages, which thus must be labeled kosher for Pesaḥ. Even if the animal was slaughtered before Pesaḥ, when there is no problem if it was fed ḥametz, supervision is nevertheless required to ensure that no ḥametz crumbs fell into the meat between the slaughtering and the packaging.
The same applies to eggs: as long as the eggs were bought before Pesaḥ, they are entirely kosher for Pesaḥ; that the hens were fed ḥametz makes no difference because it was not prohibited when eaten. The halakhic status of an egg that comes from a hen that ate ḥametz on Pesaḥ 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, one must be stringent and refrain from buying such eggs. In practice, there is no supervision on eggs laid during Pesaḥ, so it is best to buy eggs laid before Pesaḥ.
A problem also arose with regard to the markings stamped on each egg. Some are concerned that these markings contain ḥametz and that a drop of it might fall into Pesaḥ food. But I heard from Tnuva’s Rabbi 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 Pesaḥ with a stamp that contains no ḥametz. (The stamp’s pattern is several stars.)