'sleek-finned' originates from Modern English compounding of the adjective 'sleek' and the adjectival form 'finned' (from 'fin'), where 'sleek' meant 'smooth, glossy' and 'fin' meant 'a thin limb or appendage used for swimming.'

'sleek' developed from Old English words such as 'slic'/'slec' meaning 'smooth' (from Proto-Germanic *slikaz). 'Fin' (the appendage) entered English through earlier Germanic and Romance influences (ultimately related to Latin 'pinna' for a feather/wing in some pathways) and was used in Middle English as 'fin(finne)' before stabilizing as 'fin' in Modern English. In Modern English compounding productivity produced descriptive compounds like 'sleek-finned.'

Individually, 'sleek' originally meant 'smooth' and 'fin' referred to a feather- or wing-like appendage; combined in Modern English they specifically describe animals or objects as 'having smooth, streamlined fins.'