In a flaming manner; with flames, passionately, or in a conspicuously fiery way.
From 'flaming' plus the adverb-forming suffix '-ly.' The base adjective 'flaming' comes from 'flame,' and the adverbial form allows describing actions or states done in a fiery or passionate manner.
Adverbs like 'flamingly' show how English's '-ly' suffix is so productive that we can add it to almost any adjective to create an adverb, even rare ones—a speaker can be 'flamingly angry' and everyone understands it perfectly, even if it's not in the dictionary.
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