There is no free app that both keeps your own chats genuinely private and hides them from whoever is holding your phone. The "secret chat" apps advertised that way are almost always vault apps dressed up as a calculator, and they hide a conversation from a person, not from a network — which is why they are the single most common thing we get asked about and the single most common sign that someone is being monitored or is doing the monitoring.
If you want privacy for your own messages, the free options are the real ones and they do not need a third-party tool: Signal (free, open source, end-to-end encrypted by default), WhatsApp with disappearing messages turned on, and Telegram's secret chats. None of them can be bypassed by a parental-control dashboard, and none of them require you to install anything from outside an app store.
If you are a parent checking a child's Android phone, the free first-party tools come first: Google Family Link shows which apps are installed and lets you approve or block them; Android's own Digital Wellbeing shows daily screen time per app. What neither shows is message content. If you need that gap covered, Ultimate Phone Spy runs on Android 4.0+, Windows and Mac and lists every installed app with install dates alongside SMS, call logs and web history in one dashboard (installed apps, system requirements). It has no iPhone support, because iOS gives no device-level access to app or message data, so any product claiming live iPhone chat reading is not telling you the truth.
The line to hold: installing monitoring software on another adult's phone without their knowledge is illegal in most jurisdictions — the US Wiretap Act and state privacy statutes, the UK Computer Misuse Act 1990, GDPR in the EU, plus stalking and domestic-abuse statutes that treat covert device access as an aggravating factor. Legitimate use means a device you own, a minor you are legally responsible for, or a company handset covered by a written, disclosed policy. If the question is really about a partner's phone, the lawful routes are their consent, a court order, or a licensed investigator, and no app shortcuts that.