Thanks for the link Patches.I searched for awhile and couldn't find another black and grey example like the OP piece.But it looks familiar;I think I've seen another some years back.
Anyway,I did find another right facing Phoenix at the Imperial War Museum site.I'll post that example here.
Here is the description from the site:
Badge: A purple Phoenix with red eye and tongue, its wings outspread, rising from red flames on a silver wire circular background within a blue border. White cloth backing. Looks right.
Badge worn by HQ staff of Admiral Lord Louis Mountbatten, Supreme Allied Commander South East Asia (SACSEA). The badge signified Allied might rising from the ashes of the Japanese occupied territories of Burma, Malaya, China, the East Indies and South Pacific. SACSEA was set up at the Quadrant Conference in August 1943. The new command was to control all operations and command all forces in the South-East Asia theatre. Admiral Lord Louis Mountbatten was appointed Supreme Commander on 25 August 1943, the US Lieutenant-General J. W. Stilwell (Commnder CBI (China Burma India Command) was made his deputy. Initially the headquarters were based in Delhi but were moved to Kandy in Ceylon in April 1944 and eventually relocated to Singapore in 1946.
Apparently this emblem was worn mostly by British and Colonial troops,along with some worn by US personnel.