If you are sitting in space, far from any planet or large gravitational object, can you be sure that you're in a flat spacetime? Is it possible that some very distant object is heavily warping spacetime, but because it's so far away, it's acting uniformly on the area around you, so there is no way to detect that you are in warped spacetime.
Your question, no offence, is too vague to be answered in specific terms. If you take a small enough space, it can be locally flat, but the nearer you are to a given mass, the smaller you will need to make that space in order for it to stay flat. It depends on the mass and how far you are away from it.
I appreciate doetoe's comment regarding my answer as it improves my wording:
Local flatness in the sense used by physicists doesn't say anything about flatness: it holds for any metric (flat or not). In fact (intrinsic) curvature is an absolute quantity, and it is defined at every point. Your second remark is a good one: a way to detect curvature at your location would be to look at triangles, but a single one is not enough if curvature is not constant.
Put another way, how do you know how warped spacetime is around you? Can you only measure it based on how other objects gravitational are accelerating towards you?
You can draw a triangle, and if the total number of internal degrees is greater than 180, then you are in K = +1 positive curvature space, if it is less than 180, you are in K = -1 negative curvature space.
Put yet another way, is the curvature of spacetime absolute with some points in space having 0 spacetime curvature, or is the curvature relative to other areas?
There are no absolutes, it all depends on the scale you use to measure.