In the book Animal Farm, did the character Boxer ever get freedom? How?

He was not of first-rate intelligence, but he was universally respected for his steadiness of character and tremendous powers of work.

In George Orwell's Animal Farm, Boxer the horse is a strong and hard worker. In fact, he is arguably the hardest worker on the farm:

He seemed more like three horses than one; there were days when the entire work of the farm seemed to rest on his mighty shoulders.

Boxer has a strong work ethic, and because he is not smart enough to think for himself, his solution to conflict is to keep working harder. He even keeps working when he is injured, as he looks forward to soon retiring. While working on the windmill, eventually his strength fails. When he collapses, the pigs claim they will take him to a hospital to heal—but the writing on the side of the cart that arrives for him instead implies they are sending him to a glue maker to be slaughtered. At the end of Animal Farm, Boxer is dead.
Boxer dies and therefore is unable to achieve freedom. He never reaches retirement, and he dies at the hands of the pigs, who profit from his slaughter. He tries to escape the cart but has lost his strength.
Boxer's death means he did not reach freedom—however, one could argue that death itself is a kind of freedom. In death, Boxer is no longer at the mercy of an oppressive government. He no longer has to work. In death, Boxer is free from a life of hard work and oppression.