Read what the Shooting Blazar Dragon says:
1 Tuner Synchro Monster + 2+ non-Tuner Synchro Monsters
Nowhere do you see here “Dark Synchro” written. You cannot mix them. Not only that but Dark Synchro Tzolkin (Level 12 while on field) + Shooting Star Dragon (Level 10 Synchro) + Phonon Dragon (Level 4 Tuner Synchro). Even even Tzolin was treated as Level 0, 10 +4 = 14 not 12.
A Dark Synchro monster has never been used as material in the anime or manga for synchro material.