...if he does a shrinking charm on his circle, so it looks like it's about a foot smaller, it shouldn't actually get any smaller but the cultists might become mistaken about where its border is. 

It takes him five tries.

The cultist doesn't notice.

And now he has an even smaller space to practice in. He goes back to practicing anyway.

Next loud noise gets ten seconds of flamethrower.

If he just takes off his clothes so they won't be annoyingly on fire does anything happen?

No, that seems to be allowed.

He'll fireproof them next time he can talk, it just isn't something that comes up much and he can't pull it off nonverbally. Do they keep increasing durations of flamethrower?

Yup, five seconds more each time he makes an Apparition crack sound.

Which he'd stop doing given other things to do. 

Eventually he successfully jumps a foot.

That'll get him another burst.

He's so thrilled he doesn't care. Also maybe eventually they'll be careless and step too close.

After an hour this cultist is replaced by another cultist.

Their captive demon is trying to repeat successful Apparition within the smaller circle.

The new cultist has been informed of how many increments of increased flamethrowing they're up to.

He really does not like these people and is not going to feel bad at all when he gets one to step close enough.

They don't seem to have a stepping close to him protocol going on here.

After this cultist has been meditating at him for an hour she leaves and is not replaced. It's dark outside.

He could make light but he doesn't bother. He practices until he can reliably hop across the circle and then he starts mentally picking apart the language they were chanting in.

A loud noise is apparently sufficient to get a cultist out of bed to flamethrower him some more.

Well in that case they're not getting any sleep.

They look really tired by morning. When the sun rises there is more chanting.

One of them chants wrong and gets five seconds of garden hose to the face. It looks unpleasant.

Poor cultist. He feels so sorry for them. He Apparates around his decoy circle, hop hop hop.

Flamethrower.

Yes, he follows their philosophy of deterrance. His philosophy of deterrance is to be really impossible to deter from things. 

Continuous hopping. If he were human he'd be exhausted and leaving chunks of himself behind.

They have to replace the fuel in the flamethrower.

The wielder of the hose murmurs very softly to some cultists in what is probably English.

It takes him two hours to get a sound-amplifying spell working nonverbally. Might've been faster if he had stopped hopping but he does not intend to do that.