When I left the hospital I could not imagine how I'd ever be able to tandem BF by myself, but now I do it daily and it's not bad at all. Very doable. For me, the most important thing is advance preparation. While the babies are napping or quieting playing (aka my hands are free) I prep the bottles (since we supplement), burp cloths, pacifiers (we use these to calm them on breaks during the supplemental feeding, and afterwards to encourage napping), nipple shield, and anything else I want or need to have access to during the feeding (remote, phone, water, snacks, etc.), since once you start you're basically tied down to that spot until the babies are done and/or asleep. Once I'm prepped I change both babies, then get set up on the couch with the twin pillow and one baby, then grab the other baby from the couch next to me.
I don't burp them during the BF portion because my babies haven't needed it, but will during the supplemental formula feed. I'll generally burp them once or twice while they're taking the bottle, and I'll burp one, set him down, then burp the other. If I'm still nursing one baby and the other finishes, I use my free hand to give him the bottle. If he needs to burp I give him the pacifier and soothe him until his brother finishes nursing and then I can burp him. I have not yet mastered burping a baby while the other is still latched, but I know it can be done.
You can do it, it just takes practice and organization!