By definition, a level set of contact type admits a contact form obtained by contracting the Hamiltonian vector field into the symplectic form. In this case, the Hamiltonian flow is a Reeb vector field on that level set.
The definition of a level set of contact type allows for the creation of a contact form by applying the Hamiltonian vector field to the symplectic form.  In this specific instance, the Hamiltonian flow results in a Reeb vector field on that level set.