Well, this may not be the easiest way to hunt one, as the rate at which you encounter the Pokémon themselves is horrifically low, but it is certainly an interesting way to shiny hunt one.
If you start a curry shiny hunt in the Glimwood Tangle, data shows that Authentic Sinisteas actually have a significantly higher encounter rate than Phony Sinisteas. Meaning that if you encounter a Sinistea by curry hunting, it will most likely be authentic.
Again, I am a hardcore curry shiny hunter myself, and curry shiny hunting takes loads of time and dedication, but if you want a way to hunt Sinistea that will most likely help you end up with an Authentic one, curry shiny hunting is the way to go.
Curry hunting is a full odds hunt, so it will naturally take a lot of time. Also, there is no way to guarantee which Pokémon will spawn after you make a curry, so you will most likely phase out before you get your Sinistea. But if you have the time, determination, and need for a shiny Sinistea, then I highly suggest doing a curry hunt for one.
Cheers!!