What procedure would be best for my weak jawline/ flat face?

I need to see photos in order to give a proper answer to your question.           

Without photographs, it's impossible to give any opinion. Chin implants are performed for patients who have a weak and recessive chin profile. Chin and Cheek implants are composed of Silastic, and are manufactured in a variety of sizes and shapes. Chin implants are inserted through a sub mental approach under local anesthesia, while Cheek implants are placed through an intra-oral approach directly over the gum line and placed on the maxilla under a brief general anesthetic. For many examples of cheek and chin implants, please see the link below

There are a number of different options that are available, including implants, temporary like fillers or longer. Also, you may be a candidate for other procedures if you say you cannot close your lips. I usually sit down with my patients, listen to what concerns them, give them the alternatives and pros and cons and go from there.