In The Feeder
Phoebes and the other flycatchers do not use the bird feeder at all since most of their diet is insects.
In The Landscape
All the flycatchers have a diet nearly exclusively on insects. They do eat up to 10 percent of their diet in small fruits. The flycatchers as a group will eat sumac, poison ivy berries, bayberries, dogwood, holly, hackberry, lantana, blueberry, cherry, grapes, olive, blackberry, pokeweed, mulberry, spicebush, Common persimmon, Virginia creeper, viburnum, elderberries and sassafras.