In all honesty, probably not very long. I spend a lot of time outdoors, and I’ve done my fair share of camping, and have even taken a wilderness first responder class, so I consider myself a least slightly well-versed in some wilderness survival techniques. The major problem in this particular scenario is the lack of a fire making tool. Now, we are allowed a knife, which could possibly be used to help start a fire, but this is very, very difficult. I’ve tried it several times, with no success. So, I don’t see my chances of making a fire in this scenario to be very good. Without fire, I really don’t have water. Granted, some water is allowed, but 200ml is not very much to depend on, especially in a rain forest environment with high temps, where I would be sweating heavily. Without the ability to boil more drinking water, I’d give myself only 2–3 days. (If I was allowed a flint and a good pair of hiking boots, I’d up my chances to a week or so.)
That being said, here’s what I would try to do: First of all, find some high ground (a hill, mountain, or tree) to get a better sense of my surroundings. If I saw a town, village, or any signs of settlement, I would head that way, taking several stops along the way to reassess my sense of direction. If I didn’t see any signs of development, I would look for rivers or coastlines, because these are areas where settlements are most likely to occur. I would work my way along the rivers edge or coastline until I hopefully came upon a settlement. Getting to an area with people and resources would likely be my best chance of surviving the scenario.
Also important: I would do my best to keep dry (not swimming across a river, or doing my best to avoid rainfall). Getting wet could be a quick way to lose body heat (it’s cold at night even in a rain forest), which could be detrimental in this type of situation.
I hope I never have to put any of this to the test.