Can I have a sliding genioplasty after I've had a chin implant?

The direct answer is 'yes'. In fact there are circumstances which require that type of combination to achieve the proper projection and contour. The type of implant material can be modified as well. 

 Hi, non smiling photos of your before and after your chin implant surgery along with the chin implant designation would help in the evaluation.  The sticker will tell the model, style and allow the projection ( thickness) to be determined.  I say this because I have used silastic anatomical style chin implants, or similar ones early on) for the past 30 years.  They have the ability to correct really weak chins, so I'd be curious to see the dimensions of the actual implant that was used and the aesthetic result that was obtained.   In my humble opinion, a silastic chin implant is far less invasive than sliding genioplasty that requires bone cuts, metal screws and plates.  I also have a difficult time understanding how you can cut a small bone (since that's why the chin is weak in the first place), move it around and somehow create a significant "increase" in bone volume that will provide the required forward projection to correct the weak chin.  In theory, if you wanted a sliding genioplasty at this point you would need to remove the chin implant before or during that procedure. Hope this helps.