What flowers work well for an alpine garden with poor soil?

Don't plant species that need fertile soil and constant moisture there - they'll just die. For poor soils, sedums, sempervivums, armeria, phlox, saxifrage, and edelweiss work well. All these plants are adapted to growing on rocks and in arid areas, so they get by with minimal nutrients. The main thing is good drainage so water doesn't sit around.