Smoke and flame are produced due to different reasons.
A flame is produced when the gases released when a fuel is burnt are combustible. These gases then catch fire which we see as a flame.
Smoke is a result of partial combustion or some leftover unburnt particles. These tiny, unburnt particles get released into the air alongwith the gases of combustion and get mixed with the air which we see as smoke.
These two things can happen independently and thus occurence of one event does not guarantee the occurence of other.