I'm not able to replicate your problem.
(1) Spineboy
(2) Add a child BoneFollower GameObject that follows his gun. default settings. follow: bone rotation, z position, skeleton flip.
(3) Add a particle system to that GameObject
(4) enter play mode.
(5) Particles point away from the camera.
(6) Skeleton.FlipX = true;
(7) Particles still point away from the camera.
Alternate setup:
(3) Add a child ParticleSystem GameObject to the BoneFollower GameObject. Rotate it so it points in the gun direction.
(4) enter play mode
(5) particles point in the gun direction.
(6) Skeleton.FlipX = true;
(7) Particles still point in the gun direction.
