I am sorry to hear you are worried about Jack's eyes, and that you are close to these terrible fires. I am a veterinarian and will do my best to help.
Absolutely this could be irritation from the fires.
Is he squinting at all? Can you look to see if his pupils appear normal size? One concern is that he could have a corneal ulcer, where the clear cover of the eye, the cornea, is scratched or compromised by the smoke. If he has an ulcer or cornea damage, he would probably be squinting, and the pupils of the eyes might look very small. It is always a good idea to have your vet check to be sure his corneas are intact.
If his pupils appear normal, you could get some Refresh eye drops, and put them in the eyes a few times a day. After a few hours, flush the eyes with artificial tears, or saline solution and then put the Refresh drops in again. The idea is for the particles in the smoke to stick to the Refresh drops, and then regularly flush out the Refresh, and irritants in it, out of the eye, and then repeat.
You can also try Terramycin eye ointment in the eyes twice daily. It has tetracycline which is antibiotic and anti inflammatory. It is available without prescription in places like feed stores, pet stores, or online (except in California).
I hope both the smoke and his eyes are better soon. I am in New Mexico, and we are getting the smoke here, too, but not nearly as bad as what you must be getting.
Let me know how he is doing. Rebecca