I think the first trace of "the conspiracy" in general shows up in the 1100's. This is as far back as one can trace the Machiavellian writhings of the House of Guelph-Este. This is not exactly the question I believe you are asking, however. I believe you are asking when the conspiracy expanded to hide the shape of the earth began. This was somewhat later.
wait, now I'm confused again. Are you saying that every conspiracy, ever, has in fact been one big conspiracy? and, at some point they decided to add "lets tell them the earth is round" to the list of lies?
A note on "Ski"s comments about cartography and exploration, if the goal was to dupe the most money possible out of as many governments as possible for as long as possible by making "new maps", wouldn't the ideal shape be an "infinite disc", not a "finite sphere"?
Why would these con men choose a shape that would inevitably run out of empty space for them to "invent new continents" on for fun and profit?
please help, this conspiracy is getting bigger, and it's veracity is getting smaller. Please tell me you have something else.