Firstly, they are almost certain to be
extremely futurist. As in, the slightest overperformance of industrial quotas would probably cause dedicated Illuminists to put on their Phrygian caps and start dancing in the streets and bowing before a giant statue of Reason, because it means that the future will arrive slightly sooner. I expect that Illuminist newspapers and magazines would include sensationalized accounts of every new invention, complete with speculation on its possible uses.
As for industrialization, I think it is rather hit-or-miss as to whether the Illuminists are more or less industrialized than the OTL USSR as of 1938. The absolute zeal for the future, coupled with likely state subsidization for factory construction, would suggest that they would be more advanced. Moreover, the Illuminist armies and security forces would likely partner with factory owners to enforce maximum efficiency and compliance. This would work in parallel to the OTL role of the US Army National Guard and militias like the Pinkertons in suppressing the late nineteenth-century labor movement. "Wrecking" might be a crime in the Illuminist world like it was in the OTL USSR, so that slow workers can be prosecuted to inspire speedy compliance in the others.
In the military, I think that the uniforms will look like a cross between East German and late-Soviet equipment, and stereotypical 1960s-1970s science fiction garb. I think the Illuminist army will have East German helmets except with the faces enclosed by respirators and gold-plated visors, that their uniforms will borrow the late-Soviet obsession with oversized headwear and grandiose medals, and that the overall style of uniforms will look like something from 2001: A Space Odyssey or the 1980s Star Trek films. For the branches of the Illuminist military, I think they will have the Ground Force, the Naval Force, and an Aerospace Force. The countries of the Illuminist world will probably be organized into a Warsaw Pact-style alliance such that soldiers from any two countries are practically interchangeable.
Reviving Roman culture seems somewhat likely, with Russia having seen itself as the Third Rome, but I think the Illuminists would be equally appreciative of Classical Greece. They might even create an Olympics equivalent, and lavish praise upon the winners because of their ultra-meritocratic approach. On the subject of meritocracy, creating a Republic of Virtue is a likely goal for the Illuminists, and the social elites in the Illuminist world will probably see themselves as a virtuous "body of the elect" composed of rational supermen. This would create a parallel to the RU's "Saven." The local Robespierre fanaticism might lead the Illuminists to build TTL's Robespierre Monument. The Illuminists, however, probably care enough to build the monument out of a more durable material so it survives longer than three days.
Economically, I think the Illuminists will take after Pinochet's Chile. That is, they will privatize most things and break up collective landholdings for sale on the market, but create a technocratic class of local and foreign experts to advise the regime in its economic and social policies. I think the Illuminists will probably subsidize industrialization and offer excellent deals to companies who are willing to build the regional geoengineering projects and rail networks. The governments of Illuminist countries would probably partner directly with companies, but would not take over or create state owned industries. Moreover, I think the Illuminists will create a common market and have a shared currency, called something like the Reason (locally translated in each country). Lastly, I have described a possible Illuminist economic policy in a previous post that explains that, being a revolutionary movement, the Illuminists would be aware enough of the potential power of mobs that they would pass Laws of Maximums to ensure that the needs of the citizens are met to avoid grain riots. However, this could lead to unintended consequences, as the citizens protest to have maximums placed on more commodities. By the 1990s, the Illuminists could be having television riots so the Kremlin levels a fixed maximum price on television sets.
As for the flag, it will probably either be a red flag with a charge in the corner, or a French Revolution-inspired tricolor. I have already posted my proposal in this thread, in post 1299, back on page 65.