When was the first union made?

The Union Jack is the flag of Great Britain. I will assume you mean the Union vs. the Confederate flag of the American Civil War. Although Kansas attained status on January 29, 1861 as the 34th state, Ft. Sumter was still flying the 33-star flag when it was bombarded in April. Therefore, it could be argued just as effectively that the first official flag of the U.S. (Union) Army of the Civil War was the older, 33-star banner or the newer, 34-star version. However, the official flag of the Union when war broke out was the 34-star Kansas-inclusive version adopted at the end of January, 1861. Many versions followed, some representing states and others brigades and various military units.