How long can a jammed joint in your foot take to heel?

The time varies. This depends on how severely injured the joint is, how is was injured and which joint is involved. In some instances, permanent damage can develop over many years causing arthritic change to take place. Sometimes it will improve within 2 weeks.
Several weeks. Typically a jammed or sprained joint can take a week or two to heal. However, for severe pain or lack of improvement, see you dr to make sure nothing more seriouis is going on.