Sounds like a symbolic thing to me. Is it cultural? In any case, it does not sound in the least demonic: one is praying a prayer to God in writing, and then burning it to symbolize its having been sent, or its leaving of the decay of this temporal world and entering in to the mind of God who dwelleth in the eternal and incorrupt Heaven. Similar things are done by pinning fabrics to statues of saints, writing confessions down and then burning them, etc. without being demonic.
Of course, if you are uncomfortable doing it, don’t do it. It doesn’t make the prayers get to the all-seeing living God any faster; he sees them before you have written them, and moves the tip of your pen. But, the symbolism is mostly harmless, in my opinion. (Burning a list of sins is completely harmless and quite attractive in symbolism; burning a prayer could be interpreted in a poor light by someone completely set on making it look demonic, but, interpreting it as neutrally as I can, is merely a symbol that the prayer has been sent forth. Remember that fire is not demonic, however often it may be portrayed as such, because Hell is full of fire and terror, but God is light, and, our main experience of light is from fire - the fusion fire of the Sun, and fire of oxidative combustion on earth: it was our sole experience of Light, before we had electricity.)
I’m known for rendering harshly conservative judgments against these sorts of practices (anything with any link to the occult), and for connecting things to the occult in somewhat credulous ways, but, for this one, I judge it to be inoffensive.