Do gear train cogs exist (for driving a cog from a motor)? Are there any gears made that can directly drive a cog? Specifically, there should be a rounded "flower" gear that could interface directly and reasonably efficiently to a bike cog. However, I cannot find any examples of this.

These cogs are very unlikely to exist. A proper gear-to-gear transmission uses an "involute" tooth profile, which is shaped so that the gears maintain a constant relative rate of rotation. A side effect of this design is that the tooth surfaces approximately roll against each other. The flower-cog pairing would have a large amount of slip (and thus friction/wear) between the teeth as they move past each other.

The inner rollers on a bike chain are there to provide a rolling contact between the chain pins and the cog teeth. It might be possible to design a mechanism with a set of rotating round "teeth" attached to a carrier-cog, but this greatly increases your engineering complexity.