This question isn't exactly timely, but I'm curious about it. Were there any athletes from colonies participating in the Olympics? If so, did they compete under their own country or under the flag of the Colonial Power? Did Algerians participate for France? Did Koreans participate for Japan? How about Austria and its European possessions? What about a place like Australia that has a status between that of a colony and an independent nation in 1896?
Koreans did participate under the Japanese flag. Sohn Kee-Chung was a Korean who won a gold medal for Japan in 1936. Many colonial possessions also submitted their own athletes under independent committees. In 1900, you had Australia, India (part of Great Britain), and Norway (part of Sweden). You also had independent teams from Austria and Hungary, despite both being part of the Austro-Hungarian Empire. However, even today you have weird things with non-countries participating. Hong Kong, Puerto Rico, the Virgin Islands, American Samoa, Guam, Palestine, and a ton of British Overseas Territories have their own Olympic teams.