The short answer is absolutely not. In fact, the platform believes quite the opposite. It really sounds very much as if it would like to do away with the capitalist system altogether. For example:
Wealth belongs to him who creates it, and every dollar taken from industry without an equivalent is robbery. “If any will not work, neither shall he eat.”
This is very much of an anti-capitalist statement. It implies that the managers and owners do not do any real work and are only stealing from the people who really do work.
Overall, the platform implies time and again that the rich have too much money and that the farmers and workers do not have enough. It does not actually say that it aims to redistribute wealth, but it clearly implies it in statements like the one above and in calls for a graduated income tax, etc.
Omaha platform is the popular name for the declaration of policies and demands of Populist Part called Populist Party Platform released on July 4, 1892.
At the time of release of platform the terminology of capitalism as opposed to communism or command economy were not evolved, and the platform did not specifically used these terms. However, the sentiments of the platform about distribution of wealth are very clear. The platform has criticised very clearly the the skewed distribution of wealth which it claims "breeds two great classes tramps and millionaire" with land and other natural resources "concentrating in the hands of a few capitalists". It used strong language to criticize this system claiming
Fruits of toils of millions are boldly stolen to build up colossal fortunes for few.
National power to create money is appropriated to enrich bold holders
The platform believed that national wealth is created by the farmers and labour working in industries, and declared that "wealth belongs to him who creates it". Further the advocated that government should be in the hand of the people.
They sought to reduce the power of capitalists by greater direct control of economic activities. In particular the platform advocated government ownership of railroad, telegraph and telephones. Also they opposed any subsidy of government help in any form to private business. It sought to reduce the disparity between the rich and the poor bu graduated income tax.
For complete text of Omaha Platform pleas see the Website referred below.