In my experience, i didnt detect any HIF1a protein in normal cells and even most of the cancer cells under normoxic conditions. The regulation of HIF1a is very tight and the protein levels are very very sensitive towards oxygen levels so its difficult to detect HIF1a under normoxia, but story is entirely different once cells are under hypoxic conditions. In prostate cancer cells, I found 3-4 fold overexpression of HIF1a under hypoxia in prostate cancer cells compared to normal prostate calls.
As cancer cells growing in the flask in laboratory do not experience hypoxia, you might not see HIF-1a expression. If you want to do a comparison, you might want to expose cancer and normal cells to identical hypoxic conditions (or treat with cobalt chloride).
HIF1a can be expressed in normal as well as in cancer cells during normoxia or hypoxia. Normal cells mostly do this when subjected to hypoxia. While hypoxia definitely enhance HIF1a, cancer cells have the ability to express HIF1a even during normoxia (not all cancer cells). Cancer cells do so by activation of KRas or other ras isoforms. K-Ras especially regulates IRES translation