War is generally held to be bad for economies over the long term because war is inherently destructive and expensive. An army of (say) 10,000 people (I'll use this term loosely in the given context) still needs to eat, still has families to support, and still wants to live a long and useful life so as to continue to support themselves and their family. As such, you end up paying them a lot of coin (including hazard pay) to prosecute the war rather than to produce services and goods that can be consumed by your populace and build your economy. So, you're taking from your economy to support a cohort of people designed to destroy the economy of the enemy, and the enemy is doing the same to you.
No-one really wins from a war in the long term: the resentments that builds up against the enemy lasts longer than the conflict, and that reduces the desire to establish the good trade relations etc. that lead to a robust and stable economy in the long term.
BUT; in the short to medium term, there are some industries that benefit from war and the technological progress that war drives.
If your people are technologists, nothing increases investment in new technologies and research like warfare. Ultimately, you're looking for new weapons, medicines, etc. that not only make it easier to hurt your enemy but also make it easier to protect or heal your own people. If your wealthy people are highly invested in R&D, then war is going to increase the amount of public funding you get for your research, especially in the areas of novel engineering and medicine.
All those weapons, vehicles, etc. have to come from somewhere. If you already have a metallurgy technology, that means that the owners of mines are going to become very wealthy as production ramps up. The providers of raw materials will become quite rich if they can feed the war machine without becoming nationalised in the process.
Factories go from building toasters to rifles, from cars to tanks and planes. And they only have to deal with one customer: their government. This means that the production increases to a point where the owners of the factories can make a lot of money building the weapons and machines of war instead of what they normally make.
The REAL Price
None of these industries benefit from war over the longer term however for a simple reason: they are funded by the government — in other words, the taxpayers. Ultimately that money runs out because people are not producing stuff that others consume. Instead, they're producing things for a government that has to tax people to get the funds to protect them in the first place. This results in rapidly diminishing returns as people have to cut back with rations and other shortage management approaches as the normal products they consume become even scarcer as production converts to goods needed to prosecute a war.
In the long term, you impoverish your people to the point where they can no longer support the war you're fighting, either with soldiers or equipment.
That said, there is a caveat: sometimes, you don't actually need a war to drive very specific wealth. All you need is the perception of war.
The British infatuation with the dreadnought class of battleships at the turn of the 20th century was largely driven by the possibility of going to war with elements of Europe, particularly Germany. Even now, American defense contractors provide equipment to the US and other nations to ensure their readiness for war. The people who built those battleships for Britain and other nations (including the US), companies like Thales and Lockheed Martin are very rich and profitable on the back of their ability to support combat ready equipment. Research and Development actually helps these companies as well because what a government buys today is obsolete in 5 years, meaning militaries have to buy new kit later to maintain readiness despite never having used what they have already.
In short, nations can't get rich from their people’s suffering over the long term because economies need all their citizens to be productive for their economy to be strong and to grow. But, individuals can benefit from supplying weapons for 'just in case' and this is no different to what happens in today's world.