Assuming that you are using IQTensors (IQMPS) for your calculations, I would recommend the following:
(1) convert whichever tensors you want to export to just ITensors. So for an IQMPS convert it to an MPS. Or for an IQTensor (like a reduced density matrix) convert it to an ITensor.
(2) then call the "ordered" function on this ITensor to get a simple, plain tensor with a well-defined memory access pattern and contiguous storage in memory. For more information see the documentation of the ordered function on this page: http://itensor.org/docs.cgi?page=classes/itensor
auto t = ordered(T,i1,i2,i3); // <- here T is an ITensor
t(1,2,3); // <- how to access an element of the plain tensor t
(3) either use the .data() and .size() methods of the tensor object returned by the ordered function to write the tensor data to a file (binary stream) or explicitly loop over the indices of the returned tensor object and write them one at a time to a file in the way you wish (ascii or binary)