Sinusoidal infill provides great squishiness in the infill direction, but you'll still have the problem that where the infill meets the perimeter wall, it'll be less squishy than where the perimeter wall isn't touching any infill. You can reduce this effect by using a stiffer filament for that wall (if you can print with multiple filaments), by adding more perimeters, and by reducing the gap between infills (i.e. increasing the infill density). You can even explicitly design an extra-thick wall on the face that takes the pressure (the engraved face of the stamp), and then a section behind that with the squishy infill.
TBH, I'm not sure that flexible filament is really what you need for a stamp. Soft materials are commonly used for traditional stamp-making more because they're easy to etch than because the stamping works better that way. Print-making uses wooden or metal plates (the equivalent to the stamp) and produces better, more repeatable images than rubber stamps. When you're printing a stamp, you don't need to etch it, so the softness of rubber isn't an advantage for you. My outsider recommendation would be to try using a normal, rigid filament, and sand the surface to the smoothness you need. If you print with the stamp face on the bed, and your first-layer quality is really good on a smooth build plate, you can probably get better results without sanding.