In 2017 Illinois changed its law so that criminal charges for child abuse have no statute of limitations, and can be prosecuted as long as the accused is alive. This applies to all such crimes that occur after the new law was passed, and to all prior crimes on which the previous statute of limitations had not yet expired. See this news story on the change
Previously, Illinois law allowed for prosecution for up to 20 years after the victim turned 18. Since the women Kelly is accused of having abused were 16 or younger in 1998 or later, the older statute of limitations would not have expired until at least 2020.
More than 35 states now have no statute of limitations for child abuse.
By the way, for civil actions, as opposed to criminal charges, the Illinois law now says:
an action for damages for personal injury based on childhood sexual abuse must be commenced within 10 years of the date [a person turns 18] or within 5 years of the date the person abused discovers or through the use of reasonable diligence should discover both (i) that the act of childhood sexual abuse occurred and (ii) that the injury was caused by the childhood sexual abuse. The fact that the person abused discovers or through the use of reasonable diligence should discover that the act of childhood sexual abuse occurred is not, by itself, sufficient to start the discovery period under this subsection (b). Knowledge of the abuse does not constitute discovery of the injury or the causal relationship between any later-discovered injury and the abuse." (ILCS § 5/13-202.2(b))
Thus, a civil suit by one of the alleged victims might or might not be barred by time, depending on details of the date of the abuse and the victim's age.
In short, do not take a drama as a source of legal advice. Look it up or ask a reliable source.