I guess you mean the local IP of the currently connected Wifi network, right?
EDITED
In this answer, I used to suggest using the NetworkInterface in ‘dart:io’, however NetworkInterface.list is not supported in all Android devices (as pointed out by Mahesh). The wifi package provides that, but later this was incorporated into the flutter’s connectivity plugin. In Oct/2020 the methods for that were moved from the connectivity to the wifi_info_flutter plugin, and in 2021 that package was discontinued in favor of network_info_plus.
So just go for network_info_plus and call await NetworkInfo().getWifiIP().
By the way, you may also want to check if Wifi is available using the connectivity_plus plugin in flutter/plugins. Here’s an example of how to check if wifi is available.