You might also want to ask on /r/vexillology, they know dang near everything there is to know about flags.

I think the question ultimately comes down to what you mean by "the idea of a flag". People have been flying flags and flag-like objects ("vexilloloids" if we're using the jargon) all over the world for thousands of years. But if you're talking about the national flag as we understand it today -- which is to say a standardized design that represents a country, its people, its culture, and basically everything about it -- that's a much more recent concept, more on the order of hundreds of years than thousands. And it comes specifically out of Europe.

Whitney Smith briefly traces the history of the national flag in Flags Through the Ages and Across the World. He argues that the national flag was an innovation of the eighteenth century, although one built on earlier heraldic and naval traditions. European monarchs had used coats of arms and heraldic banners for hundreds of years before that, and after a while those symbols came to become identified not just with the rulers but with the countries being ruled. (The Catalan Atlas and the Book of Knowledge of All Kingdoms, both from the fourteenth century, are early examples of this process.) Meanwhile as sailing technology improved and ships were able to travel further and further afield, it became customary (and eventually a legal requirement) to fly an ensign indicating your country of origin. Naval flags had to be both easy to make and easily identifiable at a long distance, which meant they were mostly rectangular and used basic colours and patterns. These simpler types of flags spread onto land and came to be seen as symbols of the nation.

Around the same time, flags were being exported all over the world through colonialism. Most flagless countries were taken over by European powers, and those that weren't were obliged to create flags if they wanted participate in international trade and diplomacy. By the dawn of early twentieth century there were basically no independent flagless countries left, and by the time all those European colonies started becoming independent, flags were seen as just another trapping of statehood, like stamps or currency or national anthems.

I believe the last country to be without a flag for any substantial length of time was Bhutan, and it only adopted a flag so it could have something to hang on the wall at the singing of the Indo-Bhutan Treaty in 1949. (Guinea didn't have a flag for around a month in 1958, but that was only because of the suddenness of its independence. By that time the idea of a country without a flag was seen as a newsworthy oddity.)