If I was going to burn a tire for a signal (and that is a BIG if), first I would remove the air pressure. Then I would light it with a road flare (fusee). I don't know how toxic the smoke is, but I would avoid breathing it in. Most everything in a car burns dirty and black (oil, hoses, belts, seats, etc.). But you are burning up resources that you might need later.
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"We are not allowed to stop thinking"