You don't need to copy or rename the file to use JMP's text import. Use
open("$desktop/jsonfiles/zips.json","text")
the "text" option uses the CSV-style text import, which sees the Comma Separated Values in the json file and might do an acceptable import. Often not, since the records won't be on one line and the columns won't get reasonable names.
Can you share the file, or the first few lines of the file? I'd like to have that example as a test case.
What version of JMP are you using?
Craige