You didn't mention what the constriction of your barrel is. That probably matters more than whether it is fixed or not.
However, if you're talking about Foster slugs or most Brenneke slugs, you can safely shoot them through chokes as tight as FULL.
I did see TX Nimrod's link to the Benelli page saying not to go any tighter than improved cylinder, but I feel like that's more a case of the company covering their own behind.
*I have a Beretta handgun. After reading in the manual about all all the things I should NOT do with the gun, I was almost ready for them to tell me "Never fire your firearm." I think it's the result of the lawsuit-happy society we live in.
Also, there are many new kinds of slugs out there, and some of them can't compress/squeeze through a choke like the Fosters/Brennekes. Rather than a gun company making a long list of what chokes can work with with slugs and trusting the consumer to understand it, it's safer and easier to err on the side of extra conservative.
Likewise, it's hard to get a clear recommendations from ammo manufacturers--probably for the same reasons. Many make different types of slugs--some of which can be shot through tighter chokes; some of which can't. So a consumer reads than he can shoot Federal Y though a full choke, then goes out and buys Federal Z, shoots it though a full choke and messes up his gun. Then he proceeds to spread the word that Federal ammo is junk and ruined his gun.
I remember several years ago when Dixie Slugs discontinued one of their slug offerings, because despite stating very clearly that it was not to be used with choked barrel, people kept doing it anyway and then getting upset with the company.
Brenneke is among the few companies I know of that gives a clear answer as to the use of slugs through various chokes, but they also repeat in many places that this is NOT true for some of their slugs.
From the Brenneke website...
"The purpose of the ribs on the outside diameter of the slug (with the exception of the 3- inch Gold Magnum/Magnum Crush and the all brass Super Sabot which are designed for rifle barrel shotguns only) allows them, unlike most competitors slugs, to be used with any choke. As the slug passes through the three constricted areas, inside of the barrel, the Forcing Cone, Inside Bore, and then the Choke, the excess lead is squeezed into the gaps between the ribs with no damage to the barrel. Somewhat better accuracy may be noted when using the more open choke - Improved Cylinder."