Here are a few thoughts.
One of you, either you or your student, will probably have to get checked out in the airplane. If you get checked out, most likely they will see that you are a CFI and perhaps ask your intentions. If it is your student who gets checked out, your student will have to have a Private certificate before they will let your student take the plane "alone".
If you rent the plane on a regular schedule from the flight school, the school might catch on that you are giving instruction. If you are considering doing this with multiple students the school with catch on that much quicker.
Another option is to talk to the flight school, and see if they will allow you to use the plane yourself it might be part of their insurance regulations that you cannot "rent" the plane then give instruction.
Is it possible for the student to address the school and state that they want you as the instructor? The school will gain revenue from the plane being rented that they otherwise would not have gotten if you went somewhere else.
Does your situation involve one student where there is some kind of history and you two would like to stick together (work together, family member, old college friends). The school may make an exception based on the circumstance or enlighten you further as to why the instructor has to be employed by the school.
You may consider approaching the flight school and have them take you on as a contract instructor, and they provide you a percentage of the "instructor" revenue they generate off of you. Are the current instructors on W4s or 1099s? If they are on 1099s, this will be much easier for you. That way you can choose your own schedule, and get a plane without worry.
If the school is worried about you taking on additional students while there are other instructors with seniority waiting for students, you may want to assure them that is not your intention.
Does your student want to get instruction from just you? Your student could approach the flight school saying they have an instructor from which they want to learn, yet neither of you has a plane. Have the student ask the school for a suggestion.
Keep in mind when it comes to the checkride, the flight school will most likely recognize the examiner, and the student may have to provide the aircraft maintenance logs to the examiner.
If you go through the school, the student then has additional resources available to help him/her learn (other students for discussions, books in the library, additional charts (sectionals, approach plates, A/FDs) from other geographic areas.
By "interview" I assume you are referring to Charter/135/121 interview. I do not think it will be looked at one way or another during a future interview. After all, you can give instruction to someone in his/her own aircraft and never go through a flight school.
If you are referring to an interview as a flight instructor, word will get around fast, especially if there are other flight schools on the airport or at nearby airports. Word travels fast.