This is a saying about Men's infidelity and greed. They want to keep their marriage stable and still have ongoing affairs at the same time.

Men are afraid of capsizing their marriage or affairs; they want to keep both the "red flag" (wife) standing in the house and "colorful flags" (lovers) fluttering outside.

"Red flag" stands for wife, possibly because it is the color of marriage traditionally or because it is the color of the Nation's flag, thus standing for proper marriage.
"colorful flags" stand for mistresses as opposite to red flags.

There are even real estate advertisements that quote this phrase to sell houses designed for love affairs.

家中红旗不倒，外面彩旗飘飘是什么意思？_百度知道
zhidao.baidu.com/question/81847427.html - 頁庫存檔
2009年1月10日 ... 家中红旗不倒，外面彩旗飘飘是什么意思？红旗比喻妻子或者丈夫，彩旗比喻情人。
就是家里有老婆或老公，还在外风流，哈哈。
家里红旗不倒,外面彩旗飘飘是什么意思啊?_热点_雅虎知识堂
ks.cn.yahoo.com/question/3257469.html - 頁庫存檔
家里红旗是指老婆，外面彩旗是指情人或者相类似的人。只要家里面不出问题，那么
在外面就可以花天酒地！！