Unless you mean something very specific by "state machine model", there is no reason why you couldn't model conflict of interest using a state machine. The Chinese Wall itself can be easily represented as a state-machine, following the traditional BLP approach:
- a state is defined by the set of current accesses, a function associating each object to a company dataset, and a function associating each company dataset to a conflict-of-interest class.
- The transition function takes a state and an access, and if the access request is not in conflict with a current access, it is added, otherwise the access is denied.
Ravi Sandhu actually proposed an enforcement of the Chinese Wall model using a lattice-based model, and some of my PhD work was to define some general state-machine model for access control systems, including the Chinese Wall. The section 3.2 of this paper can give you a formal definition of the CW using a state-machine.
I hope that helps, and I can bring more clarifications if wanted.