Burns, Philp & Company, Limited, Sydney: A vertical slanting triband Red White Blue; on the white band a green device (a thistle?).
Source: Brown's Flags and Funnels of British and Foreign Steamship Companies.
The design is a thistle. The Brown series from 1943 and the post WW2 editions of Stewart all show the bands as vertical but Australian nautical sources do not note any change so they seem to have got it wrong.