The Center only gives advice on application for the permits required, but does not offer a proxy application service. Also, there is no facility in which Kyoto Media Support Center can permit to film at the present time. Therefore, you, on the production side must go through all of the application processes for the permits required for shooting.
If you have trouble applying for the permits yourself, the Center will introduce a company which provides shooting support services in the city. You can ask the company for a proxy application service. It may take several days after application until you get permits. Early contact with the institutions to which you will apply for is recommended for the permits required for shooting.