The reason the Thickness parameter is greyed out (Read-Only) in your form is because it is driven by the sheet metal defaults. It appears that even turning off the option to use thickness from rule in the sheet metal defaults doesn't change this.
To get around this and to have the ability to change the thickness in an iLogic Form, you will need to create a User Parameter (I called it "SheetThickness"), then create an iLogic rule and paste the code below. Make sure you do not suppress the rule and it will run each time the parameter is changed and will change the Sheet Metal Thickness.
I don't know what units you use (I use inches), since the Inventor API uses centimeters I needed to convert my parameter from inches to centimeters. That part of the code is in bold. You can change that for whatever conversion you like.
Dim oPartDoc As PartDocument
oPartDoc = ThisApplication.ActiveDocument
Dim oSheetMetalCompDef As SheetMetalComponentDefinition
oSheetMetalCompDef = oPartDoc.ComponentDefinition
oSheetMetalCompDef.UseSheetMetalStyleThickness = False
Dim oThicknessParam As Parameter
oThicknessParam = oSheetMetalCompDef.Thickness
oThicknessParam.Value = SheetThickness * 2.54
oPartDoc.Update