It looks to me that if you use the "Indoor Walk" workout type, it does not really count the flight; at least that's what I'm finding when I search the internet. I too seem to have that issue. I work on the 9th floor of an office building and I don't use the elevators. When I use the Indoor Walk workout type, the Watch doesn't seem to record any flights. But, if I don't make it a workout, flights are accurately recorded.
So I'm wondering, when I'm actually doing indoor walking, what workout type do I use to record the workout so that flights are also recorded?