You need to be really careful when using the flattening iron on tinsel because certain types (the iridescent ones) get melted on them. Those would be the ones on most G3s and G1 brides etc.
However, I´ve had success with hot water and conditioner as well. I wuld condition the hair let it stay a bit, then I´d run it under very hot water (as hot as the tap will go) for a minute or so, then rinse and possibly repeat. This hasn't exactly straightened the tinsel but it has tamed it, as in, it goes together with the hair if you don'T comb too much
I hope this helps ^^ if not, and if you want the tinsel prefect, there are some tutorials here that might help.