In my view carbon is a allotropic material, it can have various atomic structure. But in kevalr and nylon not like that. They are polymers with arimatics.
Kevlar and zylon are polymeric molecules, created by adding monomer units onto one another (in very simplistic terms it's like adding more train carriages onto a train).
Carbon nanotubes grow carbon-atom-by-carbon-atom and use a catalyst nanoparticle as a template.
This means the growth methods are completely different and a 'nanotube of kevlar' couldn't be grown.
Indeed, as Fiona and Arun have said above, producing a system, in which the aramide repeat units are connected via chemical bonds to form a nanotube-like structure is unrealistic (and would likely not yield the same properties as those of Kevlar).
Nevertheless, if the particular arrangement of chemical bonds needs not be achieved, nanotubular / nanofibrous morphologies (due to interactions between molecules or neighbouring repeat units in a polymer chain) can be obtained for many materials. To exemplify:
(although the Authors use the term "nanotubes" it refers to microstructure not chemical bond arrangement scheme)
You might also be interested in the following paper, on the use of nanotubes for reinforcing aramid materials:
Article Strong and Stiff Aramid Nanofiber/Carbon Nanotube Nanocomposites
As for your question, if we focus on a nanotubular morphology, the difficulties would mostly be related to finding a factor promoting "coiling" of the aramid chains into the desired shape (and size).