Hi Linda,
You are correct in saying that the verb disparaître is intransitive but it is not reflexive.
mes clés ont disparu = my keys have disappeared
It is not just a case of transitive or intransitive verbs which determine whether we use 'avoir' or 'être'.
According to Grevisse -
Most of the intransitive verbs take 'avoir' apart from those which indicate a movement or a change of state ( about 20 verbs) which will take 'être'.
Hope this helps!
