Is botox and filler safe after chin implant?

In general, Botox and other neuromodulators are probably fine around the area where a facial implant is located due to the superficial nature of Botox injections. These injections are generally not placed deep near the bone, which is where the implant is placed.
Injections of fillers around a chin implant or other facial implant would typically depend on the exact location of the implant and area of injection for the fillers. As an injector, I would try to avoid contacting the implant with any injections due to the very small risk of contamination and/or infection of the implant (even with proper technique). If the filler is going into the lips or marionette lines, but not contacting the chin implant, it should be fine to proceed. With proper technique, it is probably fine to even inject directly on top of the chin implant, but it would be best to avoid even the slightest risk of contamination and infection if possible.

Yes, it is okay to have Botox or filler injections after a chin implant assuming that the implant was placed under the muscle.  Injections of Botox or fillers would not penetrate that deep.  Also, the risk of infection will not be increased by having injections of Botox or filler.  Don't hesitate to contact your local dermatologist to schedule your Botox and filler injections.

[Regarding the area immediately around a chin implant]  Chin implants are usually used to improve a person's anatomy, but they cannot rectify all issues around the chin region. Therefore, sometimes a neuromodulator might be needed to relax certain muscles. Fillers might also be needed to do enhance areas very close to a chin implant. I would recommend that injections be delayed until the surgical region is totally healed.
[Regarding the areas close by but distant from a chin implant...such as the lips]  Injections are usually very safe, but anything is possible. If one is immunocompromised or the area is inflammed it might not be safe for injection as potential pathogens might spread. As always one should use sterile technique and attempt to avoid inoculation with pathogenic microbes.
At the Langsdon Clinic we frequently use neuromodulators or fillers in post surgical patients of all kinds. For more information on fillers or neuromodulators see drlangsdon.com