Plural of flatulency; instances of being flatulent or having excessive gas; the state or quality of flatulence.
From 'flatulency' (a variant or related form of 'flatulence'), with the plural '-ies' suffix used for nouns ending in '-y'.
The fact that English has multiple plural forms ('flatulences' and 'flatulencies') shows how English pluralization isn't perfectly regular—different words choose different paths!
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