Around a 10 million nanometres in length as a typical maximum, last I heard. i.e. 1cm per thread. Somewhere (recently, was it this thread?) I mentioned how winding them into longer threads (like short lengths of cotton fibre into thread, into string, into rope, etc) isn't going to give you the same strength of material (might be like graphite layers slipping over each other, if not worse).
Even if you had a 'perfect' weave of threads (or one thread that runs back and forth as a weave then turns the final corner and is the weft as well), a one-nanotube-thick weave would probably not be a sufficient ballistic protection. It may act like a silk undershirt does with arrows (tangles with the projectile, slows its penetration and makes it easier to extract again without additional underlying tissue damage) but you'd need a multi-layer/laminar solution, much as with existing ballistic protection fabrics. I think the advantage (if woven nanofabric is more advantageous than kevlar-weave/whatever) is that you can have thinner/lighter 'impermeable' (or at least sacrificially impeding) layers, allowing more/thicker interstitial padding material and/or far more other nanofibre layers to add to the impermeability/impedimenting capability, yet not be bulkier.
But that's all my surmise, it's been a while since I've been in a Materials Science lab (pre-dating a lot of the newer developments), so I'm open to being updated.