Is it legal for a LLC to give points to an employee of a company that the LLC is performing work for, in exchange for the promise of more work from that company and other companies where the employee may have contacts?

If by points you mean giving the employee an ownership interest in the LLC, the LLC may sell an interest to anyone legally competent to own an interest. However, paying an employee of another company to send you work is almost always improper [and in some cases can be considered commercial bribery or an unfair business practice] absent full disclosure to, and approval by, the employer. As to a fee for business from other contacts, this is called a finder’s fee. Again, it will depend on the actual facts of your situation to determine if this would violate some duty of the employee to his or her employer. What you are suggesting has sufficient stumbling blocks that could result in either a criminal or civil action against you and makes a consultation with a knowledgeable attorney mandatory.