Coning, possible triggers:
(1) With three fins, when a rocket experiences yaw (hitting a moving air mass can do it) and the rocket is rotated in any orientation where the fins are not oriented such that one fin is straight in the direction of the yaw, either towards it or away from it, then the fins generate an asymmetric restoration force. The axis of the recovery force is not aligned quite with the center axis of the rocket, so some rotation ensues and the recovery is not straight back in the desired direction. It shoots to the side somewhat. Therefore some coning. Using four fins instead of three should greatly reduce this case.
(2) Now take a mass, throw some spin into it, and you have a gyroscope. It wants to precess some when a force is applied that attempts to alter the oreintation of the otherwise stable axis of spin. So if a rocket in general is spinning it isn't going to want to recover to neutral when disturbed but instead will try to precess - therefore some coning.
(3) When a rocket is flying along, just like for any other aerodynamic object, there is a boundary layer. It is normally considered that at the surface of a subsonic aero object the speed of the air is always 0 with respect to the object. At a sufficient distance from the object, the air is not influenced by the object. In between there is of course a transition. The air right near the object that is substantially moving along with the object is called the boundary layer. It tends to be very thin close to the front of the object, and gets thicker as one moves towards the rear of the object. When a boundary layer gets thick enough, it tends to no longer want to flow smoothly (laminar flow, as in like layers) but instead breaks up into turbulent flow.
Now take a rocket and throw a tilt into it with respect to the flight direction. The boundary layer is going to be wrapped around the back side of the tube. Flow is going to separate most likely, causing a turbulent tail to form off the back side of the tube. This tail may be closer to one fin than another and affect the force generated by that tail. The thickness of the boundary layer by each fin may be different so the degree to which each fin is exposed to relatively clean air flow is different and the force magnitude and direction generated by each may be different.
(4) The fins on a rocket are wings. They are low aspect ratio so they are not very efficient wings, but one does have to respect structural limitations! Now low aspect ratio wings with swept leading edges generate a roll vortex off that leading edge when they are generating lift - as they will when not precisely aligned with the airflow. That roll vortex is going to try to suck the fin back into alignment. But it is also going to try to suck the tube over towards it as well. Now if there is a symmetric vortex by an equivalent fin on the other side of the tube, these forces should match. But if not, then the tube is sucked to one side. Hence some coning.
(5) The fins are wings, and wings can stall. In stall, a fin will generate less lift and a lot more drag. There is probably a case where the spin direction of the rocket is opposite the coning direction, such that the outer fin experiences little sideways force due to moving opposite the direction of the swing of the lower part of the rocket, but the inner fin is in a stall due to moving in the same direction and getting doubled sideways motion compared to the air mass. Hence coning.
(6) Consider a rocket that is long and skinny, with fins which do not protrude very far from the rocket body tube. Such fins, like all fins, lose some of their effective useful area since the flow right next to the body tube isn't clean smooth air but has been disturbed by the passing of the nosecone and body tube and is at least slightly being sucked along for the ride. That is where a lot of drag force goes - into sucking along a column of air. Now fins which do not stick far from the tube have less of their total area in clean flow and are therefore less effective per unit area. Fins which do not stick far from the tube are also often of lower aspect ratio - therefore the restoration force generated by these fins is less for a given yaw angle. Plus fins which do not stick as far from the tube are more easily completely swamped in a turbulent wake off the backside of the tube during a yaw.
(7) A tube with yaw that is spinning is going to curl its wake around the tube asymmetrically and generate a side force instead of a pure restoring force. The tube is lifting the tube to the side. So if it is spinning, a tube with a nosecone and no fins is sufficient to lead to some coning.
(8) A rocket design may not be dynamically stable with respect to coning, and therefore the very slight initial coning triggered by most anything doesn't dampen away, but instead can grow in magnitude until it becomes the readily visible big coning we see on occasion. This greatly reduces the performance of the vehicle and could under some conditions quite literally rip it apart due to the aero loads overstressing the airframe.
... Sorry this was just a bit of a casual brain dump on the subject. I haven't studied it before with respect to rockets, not in any detail, but these are just some areas to consider that come to mind.
Gerald