Start with where she tolerates things in her mouth without gagging (for some this means starting around the lips outside the mouth).
Stimulate the area with ice, brush gently with the toothbrush (I mean a sort of sweeping motion with the brush), play with the toothbrush without any teeth cleaning expectations, use a vibrating toothbrush on the area, use cotton wool, a variety of textures really. Get your make up brushes and make a game of "tickling" around the mouth area.
Get little pots with a variety of flavours and textures to play with...no eating, just the sensation e.g. cream vs crunchy crisps, curry powder vs sugar, hoola hoop vs yoghurt etc.
All done in a playful way and respecting her "no". Perhaps a doll would "try" the taste instead etc.
Do this for several days, a week is necessary, until child is very comfortable with oral area being touched. Then, move to find the point where gag is stimulated. Just on the border, don't go any further. Work on this border area until it becomes less sensitive.
Gradually, work millimetre by millimetre back through the mouth.
It is slow, patient work, but worth it.
Useful to also introduce lots of messy play at the same time (typically children with oral issues dislike hands being "messy"). Gloopy play dough. Playing with shaving foam. Finding small toys hidden in sand/rice/pasta/foam.