Do I have the legal right to kill an animal preventing my exit when I
burglarize another house?
No. I'll respond on the basis of Michigan law. Other jurisdictions in the U.S. very likely have similar statutes in this regard.
MCL 750.50b(2)(a) prohibits to knowingly and kill an animal without just cause. The act of committing burglary precludes the defendant from alleging that he or she had a just cause.
Likewise, MCL 324.43103 states: "A person shall not knowingly and willfully kill [...] or injure any fur-bearing animal owned by another person without the consent of the owner" (emphasis added). Once again, the context of burglary indicates that the defendant did not have the consent of the owner. And the argument that a dog is a fur-bearing animal can be established by an expert witness if the burglar's lawyer resorts to vexatious "defenses".
The statutory language "any fur-bearing animal" obviously encompasses domestic fur-bearing animals, notwithstanding that MCL 324.40102(1) defines animals as "wild birds and wild mammals". In fact, MCL 324.40110(1)(a) evidences the intent of permanent protection of domestic animals. It would indeed be absurd if the legislative intent (apropos of the subchapter's subtitle "Wildlife") sought to exclude domestic animals and protect wildlife only.
There might be additional, applicable statutes from that legislature.