The answers accepted do not include 'whilst he walks' which is OK in English. Lost gems spent on legend and 40 points missed ... :( Hope will change as reported.
in english, we often use the gerund in this case to repeat the subject without conjugating the second verb. in portuguese, do you conjugate the second verb or can you use the infinitive? or the gerund as well > caminhando....
With you want use "caminhando", you will need the verb "está". "Ele lê enquanto está caminhando." It comes a different meaning. Means that he is acting like that, but he doesn't necessarily do it usually.