For High Performance Liquid Chromatography (i.e. HPLC), can the column be flushed with Isopropanol (i.e. IPA)?

It will depend on the column's stationary phase. After flushing the column with IPA this should then be replaced with the mobile phase that is going to be used. Some of the more complex stationary phases do not take kindly to IPA.

(Glad you defined what you meant by IPA, I once had a student who used IPA (=beer) to develop a TLC plate!)