There is quite some literature on fracticality in architecture, most notably the research of ethnomathematician Ron Eglash on the structure of African villages.
Other fractal artifacts such as fractal textiles can be found frequently, but have not been covered extensively yet.
Mathematical fractals are infinite - real-life fractals, and especially fractal artifacts have a limited level of itearation and accuracy. To count as a valid fractal, real-life artifacts should have at least two levels of self-similartity.
In the decoration of human artifacts geometrical principles are often not applied consistently and only on a local level. This observation is especially true for the application of fractal symmetry.
While anthropologists have used rigid mathematical categories such as symmetry groups to classify decorative design, more flexible measures to calculate the actual amount of symmetry or fracticality inherernt in a real world artifact are necessary to cope with real-world objects.
There are different mathematical measures to analyze the fracticality of structures. Such measures have been used to assert the fracticality of architectural objects, including Hindu temples and African viallages. More recently such measures have also been applied to the textile domain. In the Batik Fraktal project, the fractality of traditional batik design has been measured to serve as the starting point for the creation of new batik designs of corresponding fractality.
While fracticality measures may vary tremendously depending on the underlying mathematical model, the most convincing proof of fractality, is a proof by construction. If you can give a fractal algorithm that recreates the structure in question, or a structure that is sufficiently similar, this will generally be regareded as clear evidence for the fractal nature of the artifact.