I have read in some places that there was a political/populist trend within the flagellant movement in Black-Death-ravaged Europe. How true are these claims? Further, what reading can I do specifically in regard to the flagellants and their concerns?
I am so sorry, I don't have time to do justice to your question as a whole right now, my life is nuts. However, I will say that the scholar you want is Samuel Cohn. He's the most influential voice pushing our current understanding of later medieval peasant/urban bourgeoisie actions as truly political. There are two books I'd recommend in particular:
Lust for Liberty has some scattered discussion of various flagellant movements before and during the Black Death (1260, 1311, 1349 in particular). The earlier ones had more explicitly political overtones in the sense of trying to work to get God's attention towards peace and security, but Cohn argues for political and certainly populist overtones in the Black Death ones as well especially in light of how they mobilized and catalyzed anti-Jewish attitudes and actions.
I can think of a couple other books I'd recommend on popular political actions more broadly, but they focus on other eras/movements/events rather than flagellants.