As a noun this can be used as the distinctive group phraseology for a number of ducks.
Example: A badling of ducks paddled across the pond.
The term badelynge can also be used.
Checked against my copy of The Quickaway Crossword Dictionary, compiled by H. W. Hill and published by Morrison & Gibb Ltd. Although undated, it would appear to have ben published during the period 1955-1957 (Sir Anthony Eden is the last listed British Prime Minister)