Would it be reasonable to use guitar friction pegs with a regular classical headstock? I've never seen that, all friction peg versions of flamenco guitars have a different headstock design.
It is possible but not without some modifications. Friction pegs are tapered, as are the holes they go into. The taper is what allows them to grab and hold their tune when you push them in and tighten. Classical guitars and machine tuners have a consistent diameter allowing them to turn freely so even if the diameters were about the same the friction pegs would not grab and hold because there would only be a fraction of the surface contact required for them to stay in place.
The holes for the tuners on a classical guitar would have to be reamed out with a tapered ream and then you would probably have to have a special set of pegs made since it is doubtful that standard Flamenco guitar friction pegs are the same diameter as peg holes for machine tuners on a classical guitar. It is also possible that the diameter of an existing classical guitar peg hole would not be ideal for a friction peg.
The fact that they would go in sideways instead of out of the top of the headstock like on a Flamenco guitar should not be an issue since this is similar to how violin viola and cello headstocks are.
Frankly if this is something you really want to do you would need to speak to a luthier that specializes in both types of guitars. It might be better to just design a headstock for this purpose rather than modifying an existing one.
EDIT: if you visit this link and scroll down to the 5th entry you will see photos of the headstock of a modern nylon string guitar that was constructed using geared violin pegs, not traditional violin pegs. I thought it would be of some interest.