The Fenian Brotherhood favored the Irish or Fenian Sunburst Flag as its emblem in the Civil War

In the mid-19th century the Sunburst motif was widely adopted by Irish Republicans in Ireland and beyond as a symbol of their movement and of their revolutionary ideology. 

Fenian flags tended to conform to the green of Irish nationalist banners rather than the traditional blue and usually showed a pictorial golden sunburst emerging from behind a cloud instead of from below the horizon (with or without the traditional gold Harp). Most Sunbursts were centred in the middle of the flag but some placed the image at the bottom or top-right.

During the American Civil War (1861–1865) many Irish-American regiments and units made use of the Sunburst in their flags (invariably combined with the more conventional Harp). Those that did so normally had large numbers of Fenians in their ranks or were based on previously existing Fenian organisations or groupings (this phenomenon was largely confined to the armies of the Union: for reasons of geography and ideology Confederate forces tended to attract far fewer Fenians from the Irish-American communities).

http://ansionnachfionn.com/seanchas-mythology/an-gal-greine/

From The Civil War Parlor on Tumblr