There are many aspects of the FLSA that should be understood in order to follow it properly. For example, docking an exempt employee's pay for some missed time during a workweek may result in the company losing the exempt status on the job that employee fills--including everyone in that job, which could end up being pretty costly, as overtime pay would then be required for those workers going forward.
However, the FLSA does not require you to provide paid time off work, per se. Most companies do offer paid time off work in order to be competitive (attract and retain good employees).
Other considerations would be if yours is a unionized company or if your enterprise is located in a state that requires employees in certain circumstances be provided with paid Family Medical Leave (i.e., California). Also, if you already have a policy in place that specifies that you do provide paid time off work, you should follow it consistently or else eliminate it and inform your work force accordingly.