Here's a position many FEr's take:
Planets (from Ancient Greek ἀστὴρ πλανήτης [astēr planētēs, "wandering star"], or just πλανήτης [planḗtēs, "wanderer"]) are orbiting astronomical objects. The Earth is not a planet by definition, as it sits at the center of our solar system above which the planets and the Sun revolve. The earths uniqueness, fundamental differences and centrality makes any comparison to other nearby celestial bodies insufficient - Like comparing basketballs to the court on which they bounce.
So my understanding of flat earth theory is that yes, the planets are spherical.