Is ghusl required if desire is aroused and a small amount of discharge is released—sometimes—unintentionally while performing the Sunan al-Fitra and massaging with oils to prevent hair growth?

You must avoid everything that incites desire. If you know that oils provoke it, then it is better to avoid them so that it does not lead to falling into what is forbidden. If a fluid is discharged, if it is maniyy (spermatic fluid), then ghusl (definition) (ritual bath) is obligatory. If it is madhiy (pre-seminal fluid), then istinja (definition)' (washing the private parts) and wudu' (ablution) are obligatory. If you are unsure about the type of fluid discharged, you may choose and assign it the ruling you wish.