No, it is not possible to get Red Quick Rune in Eight Inner Gates, even the Yellow one is impossible ..

Red Quick Runes is not available yet in our version and it only exist in CN version or other version of the game ( In CN, it is obtainable from Recharge Event - Max Tier), while the Yellow or Gold Quick Rune is already available in our version, it came out before as one of the items for Recharge or Spending Rebate - Max Tier also ..