I'm not sure I completely follow the question, but I’ll give it a go. There is no single “Certified Firearms Instructor” credential. Most well-known firearms instructors/schools offer their own credentials as certified to teach their system, or a part of it; examples are Gunsite, the Sig Sauer Academy, John Farnam, Gabe Suarez, Brian Hoffner, and others.
The closest thing to broadly recognized, national credentials are
NRA instructor certifications, and I’m thinking that’s what you mean. But if so, there are multiple NRA certifications specific to type of firearm and a discipline in the use of that firearm type. You can become an NRA certified instructor, but there is no encompassing “CFI.” For example, I am an NRA Certified Pistol and Personal Protection in the Home instructor. But I’m not certified to teach rifle or shotgun.
There is a basic NRA instructor’s training course, referred to as the “BIT,” that is a prerequisite to obtain any of the discipline-specific instructor certifications. So there are always at least two courses in order to gain any instructor certification. Some instructor certifications also require that you already posses the student certification for the specific discipline. For example--and I’m going only by memory here--to become a Personal Protection in the Home instructor you must have the BIT certificate, the Personal Protection in the Home student certificate, the Pistol instructor’s certificate, and then the Personal Protection in the Home instructor’s certificate.
I’m a big supporter of the NRA instruction program, and if that’s the route you’re talking about, I highly recommend it.
When you teach an NRA-authorized course, you need to do so in accordance with the policies, procedures, and guidelines of the NRA and its courseware. You must follow NRA rules because you are teaching an NRA course.
However, nothing prevents you from teaching other courses outside the NRA syllabus so long as nothing about those courses is represented as being authorized by the NRA. For example, there is no conflict in an instructor teaching an NRA authorized course one weekend, and teaching a Texas CHL class the next. The two are distinct and taught under different auspices.
Is that at least close to an answer?