Your collage plans sound very interesting! If you want to reduce the glossiness of the magazine cuttings in your collages, I would recommend brushing over the cuttings with a light coat of acrylic matte medium, such as Golden Matte Medium (this links to Blick Art Materials, and if you make a purchase I get a small commission that helps support this site).

Matte medium is easier to brush over magazine cuttings rather than entire magazine pages, so be sure to cut out your clippings before applying the matte medium. This will reduce the possibility of the page wrinkling. If the magazine cutting is already glued to your surface, that's probably even better.

If you want to paint with acrylics over top of the magazine cuttings, the matte medium will also act as a "primer", allowing acrylic paint to easily stick to the magazine cuttings.

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There are matte sprays you can use as well, such as Blair Matte Spray Coating or Golden Archival Spray Varnish (matte finish). These sprays are meant as top coatings for a variety of art mediums including inkjet prints, so they should work on magazine clippings as well.

Whether you decide to use a matte medium or a matte spray, you should do test applications on spare magazine cuttings to see how they turn out before you apply the matte medium or spray to the clippings you want to use in your collage art.