We explore properties of the long-term dynamics of particles (moonlets, fragments, debris etc.) around KBO 2014 MU69 (Arrokoth), as well as around similar contact-binary objects potentially present in the Kuiper belt. The chaotic diffusion of particles inside the Hill sphere of MU69 (or, generally, a similar object) is studied by means of construction of appropriate stability diagrams and by application of analytical approaches generally based on the Kepler map theory. The formation and evolution of the particle clouds, due to the chaotic diffusion inside the Hill sphere, are studied and the cloud lifetimes are estimated.