Rather than cancellations, I'd think delays (due to rerouting around smoke) would be more likely, depending on where you're flying from / flying to. Neither the fire near the I-405 in the Sepulveda Pass nor the fire around the I-210 is that close to Burbank to affect the airport itself, but they are close enough that they might affect some approach or departure paths. (Plus there's a possibility that some fire-fighting aircraft could be taking off from Burbank, delaying passenger flights, once in a while.)

I'm not familiar with the normal flights paths to/from BUR to places like OAK from BUR to know whether / how much they'll have to reroute. (If you draw a straight line from BUR to OAK that line crosses one or more fires before the plane has finished its climb. But planes don't necessarily fly in a straight line even without fires.) I presume flights to places like PHX to/from BUR would be less likely to need rerouting.