This could go either way, why did it burn? Was it neglect on the other cleaning companies part, or was it undressed inaccessible area's? I looked at a place that had just had a fire, and most of the system was inaccessible, they owned 5 other locations "all of them with serious access problems" they told me to clean what I could and they would address they access problems as we went. These were problems that would required tons of money to address, moving ac ducting, moving some plumbing, and opening up some walls. I agreed to do what I could, spent countless hours showing them the problems and offering some solutions.
After we went through two cleaning cycles of all the locations I got a call from a manager of the first location, saying he was a new manager and he had just done $10,000 of improvements to his exhaust system and wanted to show me personally. I went to look and the only thing that was done to the system was new wing nuts on the accessible access panels, new caulking smeared on leaky seams. It appeared to me that he spent all that money making his kitchen look new and pretty.
I went back to my office faxed him copies of all the paperwork with recommendations of changes that needed to be done to make the system cleanable highlighting all the things that they didn't do, and a note saying I could no longer service the five locations.
Be careful, don't let someone else's problems become yours, if you do take this on charge more than you normally would, now is the time to get them to agree to necessary changes that they maybe would not have agreed to.