That's a good question. I am more familiar with the International Codes than with the Uniform Codes, but I will give this a shot; they are similar
504.4 of the CA Mechanical Code (CMC) is somewhat clear that fire/smoke dampers cannot be installed in a clothes dryer exhaust duct (commercial or domestic).
CMC 504.3
does not prohibit fire/smoke dampers from being installed in a domestic kitchen exhaust duct. I cannot find any other location in the CMC or the IMC that actually prohibits the installation of a fire/smoke/radiation damper in a domestic kitchen exhaust duct.
For a commercial kitchen exhaust duct, CMC 510.1.3 is somewhat the equivalent to IMC 506.3.7 except that 510.1.3 is missing the first sentence of 506.3.7 that says "Duct systems serving a Type I hood shall be constructed and installed so that grease cannot collect in any portion thereof." IMC
implies that a fire/smoke damper cannot be installed because it will collect grease. CMC refers to NFPA 96 for it's commercial kitchen ventilation systems, the prohibition of fire/smoke dampers may be there for commercial kitchens.
Chapter 7 of the CBC
and the IBC both need a lot of work. There are many examples like this that just leaves the reader confused.