The solution you've added to the end of your post is correct. To avoid making it seem (slightly) more complicated than it is, I'd just start counting at 1 in all the for-loops (not tested):

do k = 1, nz, 1
   do j = 1, ny, 1
      do i = 1, nx, 1
         x = i + nx * (j - 1) + (nx*ny) * (k - 1)
         threeDarray(i,j,k) = oneDarray(x)
      enddo
   enddo
enddo
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The way you're varying the leftmost index fastest, goes well with Fortran's column-major order for storing multidimensional arrays.