The Hardwood billets will process faster if you use the "Use Bellows" feature of the kiln to increase the temperature.
Another large advantage for using the Kiln to produce Charcoal is that Charcoal weighs 1.00 and Hardwood billets weigh 10. Most smelting objects like the Furnace can only hold 100 weight or 200 like the Kiln so you will be able to add much more fuel (Or materials) using Charcoal since its weight is 1/10th of a Hardwood billet at 1.00.
Both Charcoal and Hardwood billets have a burning time of 10 minutes (3 minutes on a server setting of 60), and this is shortened by 1-2 minutes per use of "Use bellows". Because their burning time is the same it is recommended to only use Charcoal as a fuel source once your Kiln is operational.
Pulling out a load of charcoal damages a Kiln far less than pulling out the same amount of charcoal one at a time. Therefore, the best way to preserve the durability of a Kiln is to cook 13 Hardwood billets at a time without raising the temperature of the Kiln. One Hardwood billet will be consumed and the remaining twelve will be cooked, thus allowing you to pull out one load of charcoal.
Another option if more than 1 load of charcoal is need is to load the kiln with 20 Hardwood billets at a time, using the pull out command and adding 13 new billets to the kiln. When the piles of billets are then merged into 1 pile the heat-up time will be reduced. (the already heated billets heat up the new cold billets to about 1/3)