There's no universal timeframe after cosmetology instructor school graduation to take state boards. The requirements vary significantly by state. Some states might not have a specific deadline, while others may have a time limit, perhaps a year or two, after you graduate from your instructor program.
To find the exact deadline, you must check with your state's cosmetology board. Their website will have the most accurate and up-to-date information regarding licensing requirements and deadlines for instructor licensing.