Before the board, came the concept of the game. I am not saying that the art can't come first. It is possible to create the artwork first. And often times a designer or creator has a picture of what they want in their head before the game concept is fully finished.
In the case of the game Flags the board was changed a few times while creating the game concept. The packaging design was changed. Even the name of the game went through an evolutionary process. The point of design is to be flexible. Don't force something to work that just isn't working. If you change a rule or objective of the game, make sure the game board reflects any changes made. You will make mistakes. I know we did. Just have fun. Enjoy the process and learn as you go. Mistakes are part of what makes design work. In those "mistakes" you often find that final piece of art.