if you are using TextField then you have to add onSubmitted in your text field to detect when user press Enter key. For my case, I changed Done in keyboard to TextInputAction.Search. It also works for TextInputAction.Done too. here is a sample code
TextField(
onSubmitted: (value){
//value is entered text after ENTER press
//you can also call any function here or make setState() to assign value to other variable
},
textInputAction: TextInputAction.search,
)