Could be alternator or battery, both should be checked out, if found to be fine, I would look to ignition switch, as it will cause a multitude of weird problems.

I've been through two alternators, two batteries and a belt tensioner, realized Indy was guessing also as to what was causing the flashing battery light. I've got an 01 4.4 X5 with 130k, so it probably needed those parts anyway, but the problem persisted. New wrinkle, last week X didn't want to start, no crank, nothing, even though battery was fine with alt delivering proper volts, finally started after a few min of trying, ran fine, but battery light has not stayed on or flashed since while driving, so I'ved decided to replace ign switch this week, can't hurt, it is a cheap easy fix, about $70 for part, will update once completed.

Bottom line, I don't think anybody has a clear cut fix to BMW electrical issues, basically it's just hit or miss.
Alex