In a photo from April 2015, you can see a portion of the DIGEGA flag featuring the current seal at the far right of the picture behind the speaker. This seal is oval, with alternating blue and red sweeping arcs creating the outline of the oval in a manner representative of the Dominican Republic's national flag. At the center of the oval is the agency's acronym (DIGEGA) in dark green capital letters, with the head of a cow at far left of the acronym next to the D. The name of the agency is written in black capital letters across the top of the oval, with the name of the country at the bottom. Randy Young, 21 May 2015
The General Directorate for Livestock (Dirección General de Ganadería, DIGEGA) is the subordinate part of the Ministry of Agriculture that is responsible for overseeing the development and implementation of policies pertaining to the Dominican Republic's livestock industry. Originally created in 1948 as the Department of Livestock under the Ministry of Agriculture, Livestock, and Colonization, the Directorate has been an integral part of the system to protect and development domestic livestock. Randy Young, 21 May 2015
DIGEGA has had at least two flags that I could find in photographs online. The basic design has been the same for both, featuring the DIGEGA seal of the period centered on a white field.
Photos from 2013 (here and here) show a white flag with the former DIGEGA seal. This seal is circular: a green circle outlined with three stripes of red, white, and blue. Around the outside of the circle are written the name of the agency in black capital letters and the name of the country. Within the green circle are the head of a cow, the torso and head of a pig, the head of a goat, a chicken, a rabbit, and a red flower. Randy Young, 21 May 2015