Can you go through all 7 purifications of insight with walking meditation? Can you go through all 7 purifications of insight with walking meditation. Can you also go through the 7 purifications of insight by focusing on your steps and saying to yourself "stepping, stepping"?
Yes, of course. 


  After reciting the Pātimokkha, it seems,
  on the Uposatha day of the full moon, one of the two elders who were brothers
  went to his own dwelling place surrounded by the Community of Bhikkhus. 
  
  As
  he stood on the walk looking at the moonlight, he calculated his own vital
  formations and he said to the Community of Bhikkhus, “In what way have you
  seen bhikkhus attaining Nibbāna up till now?” 
  
  Some answered, “Till now we
  have seen them attain Nibbāna sitting in their seats.” Others answered, “We
  have seen them sitting cross-legged in the air.” 
  
  The elder said, “I shall now
  show you one attaining Nibbāna while walking.” He then drew a line on the
  walk, saying, “I shall go from this end of the walk to the other end and return;
  when I reach this line I shall attain Nibbāna.” 
  
  So saying, he stepped on to the
  walk and went to the far end. On his return he attained Nibbāna in the same
  moment in which he stepped on the line.
  
  -- Vism. VIII.244 (Nyanamoli, trans)


Note, that the seven purifications are not all related to insight directly. They are simply called the seven purifications, not the seven purifications of insight.