Kent, I think you have found a bug. I was about to write a reply expressing confusion, because I use SIDs and STARs all the time and they show the map just fine. But then I fired up iFly to grab some screen shots, and one of my commonly-assigned flight plans is now showing the behavior you describe. In my case, it appears that the SIDs and STARs were correctly downloaded for KTKI, but none of the SIDs and STARs were downloaded for T41.
The example I was going to use is KTKI > T41, with SID JOE POOL ONE and STAR BLUEBELL FOUR. I have flown this many times over many years, and iFly usually loads it up just fine.
When I select the JPOOL departure, it behaves as expected--there are multiple transitions, and I select CLL to match my clearance, expecting to also select the CLL transition for the BLUB arrival. However, this time, the Bluebell page appears with a red border, and none of the transitions are available to select. Tapping the Done button causes this message to pop up: "The STAR you have loaded does not have associated procedure data or waypoints provided by the FAA. This plate will show up in your Flight Plan, but will have no waypoints associated with it. If you want to add the associated waypoints, you can do this manually on the map and altitude planner." Also, returning to the Flight Plan page, there are rendering errors--the green box that I'd expect to be drawn around the JPOOL leg extends all the way to the right side of the screen, drawing through the distance/time/fuel numbers.
It appears that all of the T41 STARs behave this way.
Building the flight plan for my travel in the opposite direction is similar: T41 > KTKI, then select the GIFFA NINE departure and YEAGR THREE arrival. In this case, GIFFA NINE is red-bordered and I can choose no transition, but YEAGR THREE works as expected.
AP: Why are some airports' data not downloading correctly?