wolfigor
Emperor
Yes, that's one of the many options.T
You have to colonize/conquer for at least two of them. That's because once you trade for a resource, other civs don't see any point in giving you more of that resource. (Well, unless there is a corporation involved.) So, you need to trade for one Silk, and then you need to find a city to conquer that has another Silk (probably in Korea). You can also colonize the Philippines.
If you succeed to bring a galley in the Indian ocean, you can load a cataphract on to it, and sail east.
Once you reach the borders of Khmer there will be a town with golden temples: you can conquer it and you'll be able to switch to free-religion.
On one side this reduce your bonuses in Europe but cut away all negative diplomacy you have with China and Khmer:
it will be easier to commerce with them, and maybe vassallise one of them.
If China agrees to become your vassal (sometime they do, especially if they are at war with Japan) then you can get all 3 silks from them.