Problem with dullcoat

They are probably to hot for the acrylics,maybe try switching to an acrylic matte like Vallejo.I have also used Alclad.

If you don't have an airbrush,Vallejo I think is available in a spray can.

I believe Testors Dullcote is a laquer.  I have had success airbrushing over future floor was (gloss coat, decals, dull cote).  But maybe brushing on is to heavy.  I found this matrix a helpful guide

My reply would depend on what the acrylic was that you used. Some acrylics from say, Dollar Tree, basically nothing works with a brush over. As they are meant to be removeable paints. IE water washable, never mind solvents, even in spray. To know that, read the label.

I've put Alclad Matte which is a lacquer over acrylics lightly misted with no issues,but I don't think he has an AB

Brushing on a lacquer-based paint like Testors Dullcote is going to have bad results, no matter what kind of paint is underneath it.  It is pretty much a universal solvent, and the brush is adding the element of mechanical stress to the equation.  That being said, a lacquer can also be successfully used, no matter what kind of paint is underneath it, as long as it is sprayed on lightly (not applied with a brush).  But, even a rattle can tends to put the paint on WAY too wet and heavy, and it will attack any paint that it is applied over if you're too close to the surface with the rattle can.  The same would apply to the Krylon spray that you tried.  Since you're going for a matte finish, you can easily back off the model while using the Krylon.  With a matte paint, it won't matter if it's practically dry before it hits the surface of the model, which tends to produce a more matte finish, which is exactly what you want.  My advice would be to try again with the Krylon spray, and increase the distance between the can nozzle and the surface you're spraying it on.  When it doesn't go on wet and heavy, it won't have enough time to damage the paint underneath it.

I didn't know DullCote was available in a liquid form for hand-brushing.  I use the rattlecans.  I use it over water-based acrylics, like Vallejo Model Color, Andrea, Lifecolor, or craft store acrylics, with no problems.  I also use it over Tamiya's acrylics, and enamels, no problems.

Given that it is a lacquer, as was mentioned, it could be that the amount going down when applied by hand is concentrated enough to attack the color coats, compared to a coat sprayed.

I have been using Testors dull coat rattle can over my acrylic for years and never had a problem!

Dullcoat used with an airbrush is a no brainer, just dust it on in a couple of light coats and you're done. But the brush floods it on then as mentioned above, if you use any force with the bristles, you're basically mechanically removing the base color coat.

Way back "in the day" I did brush dullcoat over decals applied to Floquil paints. I just floated the coat on and let it dry. Worked great. But that's not the same as dull coating an entire finish.

But as I mentioned in my other post, there is a class of acrylic paints that are made to be washed off. They aren't a permanent paint. I'm not saying the OP used it but when used, pretty much any liquid brushed over it will have it running right off.