For the Mini Lace and Beaded Flag, it is particularly important to check that your thread colors are colorfast. If not, or in doubt, pre-wash before using.
You certainly don’t want a disaster later if the red or blue dyes run into the white (which would be very obvious), or even the blue dye running into the red (probably somewhat less obvious, but would look weird).
Checking for colorfastness is easy to do by taking a small sample of the thread, say 18 – 20 inches. Let it soak in warmish water for 15 – 30 minutes (this is so that moisture is completely taken up into the fiber). Then lay out on a white paper towel until dry. If your towel shows any sign of colors, then wash the yarn before using.
If you need to pre-wash, wind a small skein with the thread and secure loosely with temporary ties in 3 or 4 places around the skein. Put each color that is to be washed in a separate container of warm water with a bit of detergent. Let soak for at least 30 minutes, then rinse in clear water. If color still runs, consider using another thread.
I did not have any bleeding with the DMC pearl cotton thread I used, but I’d still check just to make sure. Then you can knit in confidence rather than have a nagging worry about might happen later on. A few minutes could help you avoid a disaster!