Yes, National-Anarchism espouses a socialist economic program, because the National-Anarchism movement is anti-state, and anti-capitalist. The movement calls for people to break away from state governments entirely in favor of tribal living. In tribal living, there is socialism, as each person's basic needs are cared for and the good of the group controls.
We would only know what "national-anarchism" looks like if it was put into place somewhere. Personally I think the only people who should call themselves anarchists are people who truly want no government, not people who narrowly define "government" so their ideology will count as anarchism.
Real anarchism, true absence of government won't work. Literally it won't last because people will organize to defend themselves and make agreements among each other and that will form a government. All attempts at 'anarchism' in history that came even close to success merely called themselves anarchist. Look up the anarchosyndicalists in Spain. They had organized trade unions which in territories they controlled held effective coercive power. That's a government. Most 'anarchists' aren't really anarchists they play with words and make their ideal form of government sound like it's not a government, and they may even believe they are right about it being 'anarchism'. Anarchosyndicalism for example is just a communist government with multiple organizations instead of one party and with a more decentralized and democratic set up. The fact that the multiple organizations would still have to come to some sort of agreement to coexist makes it a government. National-anarchism sounds like fascism but based on local governments hence not anarchism but nationalistic city-statism.
A socialistic economic program is all about how to support: A country, using resources, helping people to find jobs and education, progress in technology and so on... There fore, the subject of national anarchism, which is about violence, and discombobulating will espouse the socialistic economic program. Another words these are two different subject in opposite direction.
As a nationalist movement, national anarchism seeks to retain solidarity among its particular self identified group. Such a view of radical anti authoritarianism and closed community stands in opposition to the sense of the anarcho-socialist who works toward a more egalitarian society that is more inclusive than the insular national anarchists.
I do not think that National-Anarchism espouses a socialistic economic program. I think that both beliefs are definitely different in nature and do not having similar for the most part. I think that if anything, National-Anarchism is doesn't promote anything similar to a fixed economy since it is against that type of thing.
I do not believe National Anarchism espouses a socialistic economic program. For anyone actually familiar with the ideals found in National Anarchism they would know that this is as far from the truth as possible. National Anarchism is more likely to support capitalism. National Anarchism and socialism have zero ties.