It looks like the core may have been completely enclosed until the relatively recent fracturing that exposed it (the cross-cutting surface is clearly not as degraded by erosion as the main curved outer surface. And you've caught it soon enough that the core material has not been completely removed by weathering.
What is flint meal?
If you consider it just host chalk that became trapped within a flint, then I am sure you are right.
If you want to make a distinction, and consider flint meal to be a more micofossil-rich material, then you'd have to look for the microfossils under a microscope (the microfossils should separate from the powder very readily).
From a field geology perspective, I would not make a distinction. When I lived on the Surrey chalk, where flints are very common, I often found ones that included a chalky meal. I was happy to call it flint meal.
Refs (partly because flint meal doesn't come up for discussion here often):
I understood this type of flint with fine chalk inside is very rich in micro fossils so i might have a go at looking at it a bit more closely.
Very rare on the Holderness coast.
Tabfish - yes, you do need a microscope!
If you get into microfossils, they (microfossils) have a distinct benefit for you - they are sooo much easier to carry home than the big blocks you sometimes have a go at!
The question is: binocular or petrological? (or both)
In a way, you could get the best of both worlds by going for a stereoscopic petrological, but I'd advise being careful. It is easy to become a bit slapdash when dealing with hand specimens under a microscope. With a bino, such behaviour is OKish because there are no optics or mechanics below the specimen stage. If you were to be as cavalier when using a stero petro for the same purpose, debris can easily find its way into mechancial and optical components and glass can get scratched. (A removal stage covering the lower parts is a good idea.)
The big advantage of a proper petro is being able to analyse thin sections, and to do so with various modifications to the illumination (eg. plane/cross-polarized light, conoscopics, phase contrast) - enabling you to identify minerals and textures, and hence understand a rock well. That ability doesn't rely just on the microscope and knowledge, however; it also requires equipment to prepare the rock - primarily rock saw able to cut good plane and parallel slices, grinder, glass mounts and adhessive.
There is also the mineralogical microscope, which comes with tools to make indentations - enabling you to measure indentation hardness and anisotropy, both of which help ID ore minerals. That'll be low on the list of priorities. (As will electron microscope, but we can all dream!)
All types should be available on eBay/similar. But there are geology stores in the non-virtual world, and I would advise finding one of those - somewhere where you can have a play with the different types.
You have my email if you want to discuss in detail, whenever you get round to this significant investment.