DevOps lead here; technically we have 2 week sprints, but we use kanban and basically add support tickets for each item that the team needs to work on during the sprint. This means that sometimes our "burndown" is more of a level line, but when that happens my manager understands, and we either determine the type of work that would reduce it or discuss adding more capacity.
For tracking types of support tickets that come in, we try to determine which ones we can automate or heal completely so that those types of tickets dry up. Those items get roadmapped and worked down... eventually.
It works OK, not perfect but I haven't found a better method so far, and everyone's happy with my team's work.