Does this sentence go under allusion because of the mention of metempsychosis? "A mere beast of the chase flying from hunters, he was still in his metempsychosis no other than the same Monseigneur..."

Yes, because it calls to mind Pythagoras' theory of the soul.

Explanation:

Metempsychosis is a theory of the soul proposed by the philosopher Pythagoras. It teaches that the soul is immortal and that after a person dies, he undergoes different realms of ideas. The soul transmigrates from one body to another.

Allusion is also a literary device used by writers to reference something not directly mentioned. So, when the writer used the word 'metempsychosis,' the thoughts of the reader might be directed to this theory of reincarnation proposed by Pythagoras.

in the shadow of war

paine is arguying that they had tried everything before coming to the conclusion that they needed to fight for their freedom.

argument: "every quiet method for peace hath been ineffectual."

claim 1: "our prayers have been rejected with disdain; and only tended to convince us, that nothing flatters vanity, or confirms obstinacy in kings more than repeated petitioning and nothing hath contributed more than that very measure to make the kings of europe absolute."

claim 2: "wherefore, since nothing but blows will do, for god’s sake, let us come to a final separation, and not leave the next generation to be cutting throats, under the violated unmeaning names of parent and child."