After digging and testing for a bit, it appears that air units always get their Fliegerkorps rolls (in supply display), but Luftflotte rolls change, so it can be worthwhile to shuffle around Kesselring/Richthofen (8 Air) in Luftflotte HQs to airbases that are immediately doing bombing runs. Empirically, I saw Luftflotte-attached airbase have 80% air roll. When attached to a Fliegerkorp, the roll went up depending on distance, up to 88%. This is consistent with a second roll (if first failed), rolling 8 < random (10 * 2 for one HQ up). My conclusion was thus.
For ground troops, I think I saw a similar phenomenon whereby units maintained their IHQ roll values regardless of distance and had slight increases based on distance two HQs up, namely army HQs.
Using analogous tactics, then, one would want to offload army HQs of SUs in the beginning of turn and use them very close to Corps HQ (or units themselves??) provided the IHQ is within 5 for SU, etc.