What is the minimum thickness plywood recommended for internal membrane-lined gutters?

The use of plywood thickness would depend on the spacing of the support structure.

The use of plywood for guttering would normally be specific to the design as it depends on the size of the gutter, the support spacing and what depth of water is expected to be flowing in the gutter.

e.g. typically in a plywood low pitch roofing situation, 15mm F8 plywood could work with supports at 600c/c or for a plywood deck you could use 19mm F8 plywood with supports at 600c/c.