If I need to travel, should I warn the flight crew or is the risk of flying after 28 weeks far too great?

OK to fly to 36 wks. Flying per-se is not harmful to mother or baby. For those experiencing a healthy pregnancy domestic travel up to 36 weeks, and international travel up to 33 weeks is ok. The restrictions avoid unplanned delivery aboard an airplane. Check with your airline and your doctor before traveling. Don't forget to ask for a pat-down/wand instead of the scanner at security to avoid unnecessary radiation.
Don't warn crew. If you have an uncomplicated pregnancy and have never had a preterm delivery, it should be fine to travel at 28 weeks. If you are travelling, it is always good to talk to your doctor first since there are some risks, such as blood clots in your legs, that should be reviewed. Some airlines may require a note from your doctor to allow you to travel, so check with your carrier.