The challenge with the HDLC/Bell 202 "standard" is that it is poorly defined and so it results in varietal implementations. One is often left to test a questionable element against a variety of implementations to find what works best. And often "best" is not the measure but rather "what works well in this circumstance?".
Ken Finnegan, W6KWF compiled perhaps one of the best examinations of the "standard" as a Masters degree student at California Polytech. His paper can still be found on-line on the TAPR website.
If you have found that the flag byte functions without bit stuffing, then you are most likely correct. Ken points out that payload and frame checksum must be bit stuffed. From this one can infer that the flag bytes are not subjected to bit stuffing since they are not part of either. Furthermore, bit stuffing is required after every five 1's and clearly the 0x07e flag byte consists of 6 consecutive 1's so if this has worked for you in the past without bit stuffing, there exists at least some population of the implementations that agrees with your methodology. Go with that until you find a larger population of contrarians.