I agree with Su.Ki however both of the phrases sound a bit formal anyway. If this was something that you were saying in conversation it would be better to just say: I practised my speaking skills while travelling to Egypt last month.

The first one is wrong, because you can't use the present perfect tense (I've practised) with a finished period of time (last month). You could say 'I've practised my speaking skills today/ this week/ recently/ lately because these are unfinished periods of time, but you can't use this form with 'when I was' or with 'last month' The second one is ok. You could also say I practised my speaking skills while I was travelling to Egypt last month. or I was practising my speaking skills while I was travelling to Egypt last month.

I agree with Rachel B that the correct form is "I practised my speaking skills while travelling to Egypt last month." However, "I had been practising my speaking skills while I was travelling to Egypt last month" is incorrect as it stands. Because of the "had been" in the sentence, the action in "had been practising" should come before some other action in the sentence. So... I could say "I had been practising my Arabic speaking skills diligently while I was travelling [in] Egypt until a friend pointed out that I was using a book that used Iraqi Arabic rather than Egyptian Arabic." NOTE: I don't know enough about Arabic to know whether Iraqi Arabic and Egyptian Arabic are far enough apart for my sentence to make sense. My point here is that "had been" pushes an action further into the past than another action in the past. In my example, the "other action" is "my friend pointed out".