Does the Sun orbit the Milky way in a (kind of) flat or inclined orbit or more of a sine wave?
It is correct that the sun bobs "up and down" (relative to the plane of the galaxy as it orbits the galaxy, and it takes about 64 million years  to complete a full cycle, so it does pass through the plane of the galaxy every 32 million years or so (there are quite large error bars on those numbers.) 

This idea is uncontroversial, but it gets caught up in other theories that are less well established (for example the idea that there are dense clumps of dark matter in the galactic plane, that can have disrupt the Oort cloud, or otherwise cause mass extinction) or are simply nonsense (the idea that the solar system is a "vortex").

Phil Plait rubbishes this second idea on his blog, and includes some further discussion of the "bobbing" path of the sun. He notes that the disk is about 1000 ly thick, and we bob up and down by about 200 light years every 64 million years.

Lisa Randall's is a serious scientist, who would have no truck with "solar system vortices", and the ideas in her book are reasonable, but not uncontroversial. We have no evidence of dense clumps of dark matter, nor do we know exactly where the Earth was 65 million years ago. We last passed through the galactic plane about 3 million years ago, without serious consequences.