Can someone shed some light on the difference between a pure “line out” and relatively low-powered headphone amp.

For example (to cite a use-case): I still love my trusty Fiio A3 which (to my ears) sounds great as a small, standalone portable headphone amp. Let’s say I want to listen through my iPhone and I plug the standard Apple DAC - 3.5mm dongle into my phone (which by most accounts is an excellent DAC/AMP), but the Apple dongle isn’t powerful enough to power the headphones I’m using, so I output the Apple dongle to the A3 (and then plug headphones into A3).

The Apple dongle is (to my understanding) a DAC/AMP (that can power many IEMs really nicely). So am I double amping here? Am I going to damage the amp by running a non-Line out single into it? And will the sound quality be degraded (compared to a device that can output a “line out” to the amp)?