This is the basic sentence structure, “A wa B da” which means “A is B”.
A: 飛ばねえ豚 (the topic of the sentence)
飛ばねえ means “doesn’t fly”. It is a broken version of 飛ばない, usually used in very informal, male speech.
豚 means “a pig”.
飛ばねえ is a verb, modifying the noun 豚, so it means “a pig that doesn’t fly”. In Japanese, when you modify a noun with a clause, the word order is just like when you modify a noun with an adjective or a noun such as おいしい食べ物 meaning “delicious food” and 日本の食べ物 meaning “Japanese food” so the modifier always comes before the noun that is modified. For example, 昨日買った食べ物 meaning “the food that I bought yesterday” 勉強している人 meaning “a person who is studying” 昨日読んだ本 meaning “a book that I read yesterday”.
B: ただの豚 (the predicate noun)
ただの means “ordinary” or “just”. So ただの豚 means “an ordinary pig”.