Asklemmy

There isn't really any such thing as "chalky" acrylic. There are chalky watercolors, usually the sort you buy in a set of 36 for a dollar, and they aren't even fit for a five-year-old. You won't be able to get the effect you want with those.

You can scumble (dry-brush) with almost any tube acrylic, provided that it's not too wet. Avoid the runny sort of paint that comes in a bottle. Those are made for crafts, model-painting and acrylic pours. They won't be thick enough.

Use the paint straight from the tube, don't add any water, mix your colors on a palette and use a dry, stiff, round or fan brush with very little paint on it at a time. Wipe any excess off on tissue first, if you find it's going on too thick. Acrylic paint dries fast so you can make layers over layers and cover up errors easily if necessary.

Using gouache for scumbling is also possible but harder, because unlike acrylic paint, gouache will "re-activate" even when dry, so you can find that your bottom layers will start to smear and blend with upper ones. That won't happen with acrylic. You can't blend on the paper as easily with acrylic as you can with gouache; this may or may not be a disadvantage, depending on what you're trying to achieve.

Your working surface is also key; you'll need canvas (primed with gesso) or a rough, textured cold-press paper.

Lastly, don't use your best, most expensive brushes. Once you use a brush for dry-brushing with acrylic, it's pretty much ruined for any other purpose. Keep some cheap brushes that you use for this purpose only.