Badelynge (pronounced 'bad-ling') is a little-known and obsolete collective noun for a group of ducks. Notable for its inclusion in the Dictionary Of Obsolete And Provincial English, Thomas Wright's 1869 guide to English phrases that had fallen by the wayside, it is easy to see why the term 'a badelynge of ducks' is no longer in common use. Most of the words in Wright's tome have been out of use for at least a hundred years.
Alternate spellings include badelyng, omitting the final 'e', or even badling, which retains the same pronunciation but features an updated, more modern spelling.
Modern alternatives to badelynge include a paddling, raft, team, flock or gang of ducks. Other outdated and obsolete alternatives include a smeath, plump or the slightly suggestive (and thus fantastic) 'little knob of ducks'.