A flag that best matches your description was carried by the 3rd Regiment Infantry Missouri Volunteers (3 Month Service). They served in Sigel's Brigade at Wilson's Creek in 1861.
The regiment is said to have had a red flag with a depiction of a hammer smashing some chains. This is according to Wolfgang Hochbruck, Professor of American Studies at the University of Stuttgart who is cited in Tony Horwitz, Confederates in the Attic, (1998) p. 186. (One can come across flag references in the strangest places)
The Missouri State Museum collection includes the regiment's National flag. It can be seen here:
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The 3rd Missouri also was presented with a flag by the German-American community of St. Louis on 8 May 1861. The flag was embroidered with the inscription III. REGIMENT / MISSOURI VOLUNTEERS / LYON'S FAHNENWACHT (David Hinze, Karen Farnham, The Battle of Carthage: Border War in Southeast Missouri, July 5, 1861, (1997), pp. 66, 255 n. 18). A reproduction of this flag can be viewed at:
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The 3rd Missouri Regiment wore slouch hats, a grey blouse with red collar or neckerchief, dark trousers, and white cross-belts. The painting by Andy Thomas is a good depiction of the regiment in the streets of Carthage.