To achieve this, there are several possibilities :
1- Using the Text.rich constructor instead of the Text widget and then inside the constructor, you will use the TextSpan widgets that will allow you to add style through the style property. The first TextSpan directly in Text.rich and then the other TextSpan in the first TextSpan through its children property.
Text.rich(
TextSpan(
text: 'Some ',
children: <TextSpan>[
TextSpan(
text: ' Long ',
style: TextStyle(fontWeight: FontWeight.bold , background: Paint()..color = Colors.red)),
TextSpan(
text: ' world',
style: TextStyle(backgroundColor: Colors.yellow)),
],
),
)
Output :

2- The use of RichText widget . Same as Text.rich but this time the first TextSpan will be put on the text property of the RichText widget.
RichText(
text:TextSpan(
text: 'Some ',
style: TextStyle(color: Colors.blue),
children: <TextSpan>[
TextSpan(
text: ' Long ',
style: TextStyle(color:Colors.black ,fontWeight: FontWeight.bold , background: Paint()..color = Colors.red)),
TextSpan(
text: ' world',
style: TextStyle(backgroundColor: Colors.yellow)),
],
),
)
Output :

3- The use of external packages .
I propose you highlight_text or substring_highlight