Tannic acid is in several common trees. It is in the green leaves, new green bark of Red oak, not just the acorns. White Oak acorns have very little Tannic Acid. Stag-horn Sumac has a lot of Tannic Acid, I have used both to dye traps in my trapping days.
Tannic Acid is very water soluble. So, if you boil the green twigs, green leaves in water, and then reduce the amount of liquid by boiling, it will concentrate. However, inasmuch as trappers use it to dye their traps, just go to Gander Mountain and buy "Logwood Crystals", and get it ready to use without the trouble.
FYI: White Oak acorns have very little Tannic Acid, therefore may be eaten right off the tree. Red Oak acorns on the other hand have a lot of Tannic Acid, making them to bitter to eat. I have actually read that Red Oak acorns are posionous...which just is not true. Tannic Acid makes Red Oak acorns too bitter and astringent to eat as is. The Native Americans would take the Red Oak acorns and bury them in sandbars of rivers and the water would leach-out ("water soluble" remember), the Tannic Acid in a few days and then they would use them as food.