Lingustic term for three consecutive synonyms used in a sentence?
I think the term you're looking for is:
pleonasm:
the use of more words than are necessary to convey meaning (e.g. see with one's eyes), either as a fault of style or for emphasis.
Your three synonyms in a row aren't the only type of pleonasm, but this construct certainly fits the definition. An example sentence from the linked article:
"Let me tell you this, when social workers offer you, free, gratis and for nothing, something to hinder you from swooning, which with them is an obsession, it is useless to recoil ..." —Samuel Beckett, Molloy.