tensile and flexural strength depends of mechanical and physical properties of both nano-filler and matrix. but most researches are done on Al2O3 and CNTs, because of their good effects.
As mentioned from the previous comments, various factors do play a significant role in the enhancement of the mechanical properties of composites using nanomaterials.
The nanomaterials palette ranges from Carbon Nanofibres (CNFs), Carbon Nanotubes (CNTs), Graphene Nanoplatelets (GNPs), Copper nanowires and many more.
The key factors that determine the tensile and flexural properties are (a) shape of fillers (i.e. 1D, 2D, spherical, fibrous, etc), (b) orientation of the fillers, (c) aspect ratio, (d) dispersion and more importantly (e) the cohesion between the filler interface and the surrounding matrix.
This also depends on the type of matrix you use (i.e. epoxy, thermoplastic, ceramic,etc) and the filler content and quality.
Hopefully, this provides a broad overview what key aspects that need to be considered when designing nano-reinforced composite.
Complex question - there is no simple answer, as you can see from the previous comments. Concerning the problem of nanoparticle agglomeration, I recommend to read this very simple but informative paper attached.