The first flag linked is actually the battle flag/ naval ensign on The Confederate States of America. I'm probably not the best qualified to answer why we still used battle flags in that era, but traditionally, they were used as a visual rallying point and identification tool to know friend or foe. The smoke, noise and chaos of battle made these flags very necessary. Additional flags would identify individual units. You may not know the flag of the 1st Louisiana Cavalry, but you'd know the battle flag.

National flags were also used in the field of battle. The second linked picture was the first Confederate States of America national flag. Imagine that flag. Red and white striped, field of blue in the upper left with stars. Imagine a calm wind day. It looked so much like the national flag of the USA that it became confusing and even as soon as the battle of Bull Run it caused problems and commanders wanted a replacement.

In 1863 the national flag would be replaced. It essentially looked like the battle flag in the upper left and all white elsewhere. Imagine the same calm wind scenario. The all white was easily mistaken for the flag of surrender. This flag, occasionally called the Stainless Banner, was replaced by one called the Blood Stained Banner. This 3rd and final flag was adopted shortly before the end of the war. Nearly identical to the Stainless Banner it added a stripe of red running vertically along the edge so that when furled or becalmed the red was visible eliminating the idea it was a white flag of surrender.

Source : https://www.britannica.com/topic/flag-of-the-Confederate-States-of-America