I'll answer specifically for this type of mill. Since it uses grind plates, it should work. I would run a handful through to see what it looks like. Remember, you want the hulls to be more or less whole and the meat of the grain to be crushed a bit (smaller pieces mean more surface area to volume ratio). This might be fine for small batches but it you ...
Flaked wheat is your best bet. It is unmalted as well.
Otherwise, if you truly have simply dried wheat you need to perform a cereal mash on that stuff to get at the starches (even if you did crush it).
As brewchez indicated, flaked wheat can be used directly. However, if that isn't easily obtainable for you, your next best option is to use a blender. You can blend 1-2 cups at a time this way. It helps to add a little bit of water to the mix to help keep the kernels from bouncing around as much.
Just keep pulsing the blender until the wheat kernels are the ...
I doubt that the wheat was too hard for your LHBS' mill (which is likely motorized and has heavy stainless steel rollers). The issue is that the gap is too big, and the knurled rollers have nothing to grab onto. So the wheat falls between the rollers without being crushed.
Reknowned homebrewer and beer historian Randy Mosher states, "generally roller mills ...
This mill attachment looks like it might actually be usable for brewing. Most kitchen mills are not, because they will reduce the husk to a fine powder. However, without seeing the internals of this mill I can't say for sure that it would work, and I suspect you won't have fine control over the gap of the rollers.
The Kitchen Aid attachment doesn't work well for milling brewing grain according to reports from people who have used them. For one thing, it's made to produce flour, not grist. That means it mills too fine. For another, it's not meant for the pounds of grain that you'll have to mill at a time and can overheat.
My attempt with my father-in-law's corn proved that the mill was incapable of damaging the corn. I think it was probably due to the gap being too narrow.
You may need to adjust your mill to crush the corn. Also realize that a mill meant for brewing isn't going to make cornmeal or flour, but crushed/cracked grain.