The flame emoji showcases that you are in a streak with that person. This means that you and your friend have been making moves in less than 24 hours for at least 2 consecutive days. The number is the amount of days the streak is on. In order to keep the streak going, you and your friend must keep making moves in under 24 hours from when the other person played. The fire will be highlighted in red if you have less than 3 hours to make a move before it expires. Overall, it's a fun way to see how long and how often you and your friend have been playing together.