To be proudly displayed on the side of their world ships, as they leave their solar system and head towards their future.
Made on CodePen, I used a Ruby-based html preprocessor to generate this as a SVG, if you check the code you can see how loops were used, try changing the range and the angle values ( (1..8) and and angle of 45 for example), it's fun! I was inspired after ThatFanficGuy posted his artwork.
From left to right it shows their inhabited worlds in their solar system, the large one being their point of origin, the three pointed arrow is to represent the ships leaving towards the future (I may have to change how that looks so it points more forward). One little note, the big circle on the right (the future, a new planet, a big star) has the ID #wheel as I was going to put a ringworld around it. I like the idea of it being more representative of the unknown, as perhaps the civilisation is in a hurry and has to abandon their solar system, with no clear destination.
If you're in such a hurry, flag design won't be your first priority. There's nothing wrong with the civilization in question to work towards the future... ...or it's a special survey space program, somewhat akin to our planned missions to Mars; a new habitat frontier, if you wish. They would certainly need a good emblem.