A flexible packaging laminate for a microwavable package has a built-in vent for steam. The vent is formed by an outer score line through the outer layer(s) of the laminate to define an outer flap, and a smaller-footprint inner score line formed through the inner layer(s) of the laminate, so that there is a marginal region of U- or V-shape bounded between the two score lines. A patch of pressure-sensitive adhesive is disposed between the outer and inner structures of the laminate such that PSA is present in the marginal region. Pressure exerted on the inner flap or plug created by the inner score line overcomes the PSA between the outer flap and the inner structure in the marginal region, causing the outer flap to be pushed out along with the inner flap or plug, thereby venting steam through the resulting opening.