If you want to search a specific chat rather than all of your chats, this is possible too. 


Maybe you had a conversation about a specific meeting place, or they sent you their other contact number or their address for example.

iOS: Chats > Specific chat > Tap on contact info at the top > Chat Search > Type in the search bar that appears at the top of that specific chat. 

Android: Chats > Specific chat > Open the menu top right > Search > Type in the search bar that appears at the top of that specific chat.