我找到了一个方法来做到这一点。完整的代码如下，但简而言之：
1.使用LayoutBuilder确定我们有多少空间。
1.使用TextPainter模拟空间内文本的呈现。
以下是完整的演示应用程序：

import 'package:flutter/material.dart';

void main() => runApp(MyApp());

class MyApp extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      title: 'Text Overflow Demo',
      theme: ThemeData(
        primarySwatch: Colors.blue,
      ),
      home: Scaffold(
        appBar: AppBar(title: Text("DEMO")),
        body: TextOverflowDemo(),
      ),
    );
  }
}

class TextOverflowDemo extends StatefulWidget {
  @override
  _EditorState createState() => _EditorState();
}

class _EditorState extends State<TextOverflowDemo> {
  var controller = TextEditingController();

  @override
  void initState() {
    controller.addListener(() {
      setState(() {
        mytext = controller.text;
      });
    });
    controller.text = "This is a long overflowing text!!!";
    super.initState();
  }

  @override
  void dispose() {
    controller.dispose();
    super.dispose();
  }

  String mytext = "";

  @override
  Widget build(BuildContext context) {
    int maxLines = 1;
    double fontSize = 30.0;

    return Padding(
      padding: const EdgeInsets.all(12.0),
      child: Column(
        children: <Widget>[
          LayoutBuilder(builder: (context, size) {
            // Build the textspan
            var span = TextSpan(
              text: mytext,
              style: TextStyle(fontSize: fontSize),
            );

            // Use a textpainter to determine if it will exceed max lines
            var tp = TextPainter(
              maxLines: maxLines,
              textAlign: TextAlign.left,
              textDirection: TextDirection.ltr,
              text: span,
            );

            // trigger it to layout
            tp.layout(maxWidth: size.maxWidth);

            // whether the text overflowed or not
            var exceeded = tp.didExceedMaxLines;

            return Column(children: <Widget>[
              Text.rich(
                span,
                overflow: TextOverflow.ellipsis,
                maxLines: maxLines,
              ),
              Text(exceeded ? "Overflowed!" : "Not overflowed yet.")
            ]);
          }),
          TextField(
            controller: controller,
          ),
        ],
      ),
    );
  }
}

有一个更短的方法可以得到文本是否溢出的答案。

bool hasTextOverflow(
  String text, 
  TextStyle style, 
  {double minWidth = 0, 
       double maxWidth = double.infinity, 
       int maxLines = 2
  }) {
  final TextPainter textPainter = TextPainter(
    text: TextSpan(text: text, style: style),
    maxLines: maxLines,
    textDirection: TextDirection.ltr,
  )..layout(minWidth: minWidth, maxWidth: maxWidth);
  return textPainter.didExceedMaxLines;
}

你可以在pub.dev上使用flutter插件auto_size_text。当文本溢出时，你可以设置一些小部件出现。

int maxLines = 3;
String caption = 'Your caption is here';
return AutoSizeText(
    caption,
    maxLines: maxLines,
    style: TextStyle(fontSize: 20),
    minFontSize: 15,
    overflowReplacement: Column( // This widget will be replaced. 
    crossAxisAlignment: CrossAxisAlignment.start,
    children: <Widget>[
      Text(
        caption,
        maxLines: maxLines,
        overflow: TextOverflow.ellipsis,
      ),
      Text(
        "Show more",
        style: TextStyle(color: PrimaryColor.kGrey),
      )
    ],
  ),
);

我制作了自己的小部件，我跨项目使用它，它在构造函数中取Text小部件并读取它的属性。

import 'package:flutter/material.dart';

class OverflowDetectorText extends StatelessWidget {
  final Text child;

  OverflowDetectorText({
    Key? key,
    required this.child,
  }) : super(key: key);

  @override
  Widget build(BuildContext context) {
    var tp = TextPainter(
      maxLines: child.maxLines,
      textAlign: child.textAlign ?? TextAlign.start,
      textDirection: child.textDirection ?? TextDirection.ltr,
      text: child.textSpan ?? TextSpan(
        text: child.data,
        style: child.style,
      ),
    );

    return LayoutBuilder(
      builder: (context, constrains) {
        tp.layout(maxWidth: constrains.maxWidth);
        final overflowed = tp.didExceedMaxLines;
        if (overflowed) {
          //You can wrap your Text `child` with anything
        }
        return child;
      },
    );
  }
}