That's a representation of the flag, not the battle scared original.
The Union army were boring and charmless in contrast to the dashing Confederates.The Irish fought on both sides of the conflict, for the Union and for the Confederacy.
Well the flag hasn't stood up to the test of time as it looked in tatters to me, more similar to what is described in your link "By late 1862, the original colors...... were in tatters".‘I once found an old flag, an Irish Brigade flag which had been used during the Civil War by the Irish Brigade here in this country. He liked that very much, and we got it to give to the Pres…irishamericancivilwar.com
"...the colors never saw battle, though they were used during the Grand Review in 1865. The Brigade’s 1st Regiment green color remained in the Armory of the 69th in New York, until in 1963 they kindly permitted President Kennedy to present it to the people of Ireland."