“Être in fiocchi” is an expression meaning, “Être en grand costume” (similar to, in ceremonial dress).

Edit: The ‘definition’ of the term is

être en costume d’apparat, porter tous ses atours

“Costume d’apparat” implies “ceremonial dress”, while “porter tous ses atours” is “in full finery”.

(credits to jlliagre)

The young lady speaking in letter was living in a convent, I believe, and would perhaps be wearing some sort of garment for that reason. Thus they used term you asked about….
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