Incorporation was invented by the Supreme Court, and rationalized by the Due Process Clause not the clause you cite. The term occurs nowhere in the amendment.
No state shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States
No dice. Just as Article IV, Section 2, Clause 1, "The Citizens of each State shall be entitled to all Privileges and Immunities of Citizens in the several States" means no discrimination by a state against visitors or immigrants from other states, the clause you cite means no discrimination by a state between its citizens.