I haven't yet used gouache on watercolour paper, just illustration board (Bainbridge is my favourite, acid-free, cold press #180 I believe) as gouache is inflexible, fragile and I needed a smooth yet cold press surface for my work (for camera ready art, illustration),
For my watercolour work I use Arches, either 140lb or 300lb because I adore the quality, sizing and durability of it—I am addicted to it even though it's pricey.
I tape down my paper to a piece of masonite (so I can move it around easily) when I work and I find the higher quality papers don't buckle too much unless I have an uneven application of paint/water in one area. I've steam ironed and then pressed my work when the buckles were bad... not sure if this would work with gouache though.
I place the work between sheets of acid free tracing paper then on a hard surface with a white 100% cotton pillowcase on top to protect the paper from the actual surface of the iron.. I set the iron to the cotton/linen setting and steam the back until I feel the paper has an even saturation of moisture (i keep it very light, you don't want the paper actually wet, just moist) but try to avoid steaming the actual painted surface... then I gently press it with the iron on the dry setting... after it seems fairly flat I remove the tracing paper, press it between sheets of masonite, with the white pillowcases between the masonite and paper (these are washed without any fabric softener.. not sure of the chemistry in those) and a ton of heavy books for a couple of days. I get a nice flat piece of paper after.
But I don't know if gouache would flake with this technique as watercolour tends to soak into the paper more than gouache... maybe make a test sheet with the thickness of gouache you usually apply and see if it works. I think there may also be a big difference if you seal your work with a spray or medium.
I haven't yet actually 'stretched' watercolour paper because I'm leery of removing some of the sizing... and that affects how the pigment flows and absorbs into the paperflow. That may not be an issue with using gouache.
I have mounted my watercolour art to birch panels with acrylic medium... but I spray a matte clear on first and then use a cold wax medium to seal the front after.
I hope this helps.. if anything it may save your early work... taping your paper down is the easiest
