QuickDic does not transmit or share any data.
Some data like custom word lists and recent search history is stored locally on your device. That data is not encrypted and no effort is made to prevent for example other apps from accessing it. You can turn off search history in settings to avoid it being stored.
Note that when you download dictionaries they are downloaded from GitHub (github.com). These downloads are not done by the QuickDic app itself but a system component of your device (DownloadManager). Generally this download process will mean that GitHub will at that point have access to limited information about you like your IP address and the Android version your device runs. This is a normal part of any download process and not specific to the QuickDic app nor under its control.
Should the app start to use data beyond what is described here, it will be mentioned in the update notes ("WHAT'S NEW" in the Play Store).