No, you don't need any permits or permission to paint The Graffiti Bridge.

Graffiti Bridge was built in 1888

Yes, there is an exception in the City of Pensacola Code of Ordinances.

(n) Section 302.9. Defacement of property. Revise to read as follows: No person shall willfully or wantonly damage, mutilate or deface any exterior surface of any structure or building on any private or public property by placing thereon any marking, carving or graffiti. It shall be the responsibility of the owner of the property to restore said surface to an approved state of maintenance and repair within seven days of notification.

Exception: The 17th Street CSX Railroad Trestle shall be exempted from the provisions of this section. Section 302.9