Is wearing the aircast inflatable stirrup ankle brace suitable for posterior tibial tendonitis? How long should this be worn?

Yes. In most cases the aircast brace is appropriate tx for post tib tendonitis. Occasionally a brace that locks the heal itself might be necessary. With the brace, nsaid's, and some rest mild tendonitis should be better in about 3 weeks. Occasionally more aggressive tx is needed with perhaps a cortizone (hydrocortisone) injection or even surgery if the above and pt doesn't help. Good luck!
Air casts do nothing. Air casts do virtually nothing. A functional forefoot orthosis balanced to neutral is what will cure the problem. Be sure you do not stand in a mold to make it. You should be reclined and a plaster slipper cast used placing the foot back into neutral position to make it.