The herpes virus responsible for chickenpox, Varicella zoster lays dormant in nerves after the chickenpox outbreak. Shingles (called herpes zoster) break out in the region affected by that nerve or nerves, which is also why shingles are usually restricted to one body side (as nerves don't cross the spine). [NHS page on shingles]
Spreading the virus to other parts of the body is called autoinoculation. I could not find this described anywhere for Varicella zoster in healthy patients. In the related Herpes simplex, it is uncommon.
Sometimes, infected people can transmit the virus and infect other parts of their own bodies (most often the hands, thighs, or buttocks). This process, known as autoinoculation, is uncommon, since people generally develop antibodies that protect against this problem
[University of Maryland Medical Center - Herpes simplex]
Basically, the other parts of your body are vaccinated against the virus.
For Varicella zoster, it is a concern when considering immunocompromised patients (patients receiving chemotherapy, or infected with HIV, for example):
If your immune system is weakened, shingles blisters may spread to other parts of your body and it will likely take longer for the symptoms to heal, maybe lasting for months
[University of Maryland Medical Center - Varicella]
This is a bit of an unsatisfactory answer - to me, it looks like it is at the very least not a common concern. No source I could find even recommended washing hands after touching the rash before touching other parts of your body (except for the eyes), which would be a basic precaution if spreading the rash were a concern in not immunocompromised patients.