The spelling is definteily Polish. Derived perhaps from the word burka which could mean: a woollen shawl or a brawl, or from burkat (a copper vessel). Possible toponymic sources: Burkat, Burkaty, Burki...
The SPELLING is Polish. I went to school wtih a Ukrainian chap named Sawczuk who spelt his name the Polsih way, because that's how his parents spelt it in a DP camp in Germany and didn't change it in the USA. The normal transcription of Ukrainian into English would have been Savchuk.
Burkieciak have the highest number of occurences in Zachodniopomorskie (Szczecin Region). It is possible they were moved from Ukraine there just after the II WW.
And another map for you: moikrewni.pl/mapa/kompletny/burkieciak.html
Sorry for late response. Thanks beazee, so this surname might be Ukrainian? There is only 17 people in Poland with such surname, so it might be possible. Thanks again