I was able to come up with a solution using flutter_highlighter, flutter_markdown and I used Google Fonts for the monospace font.

First you need to create an Element builder to manipulate the code block in the Markdown widget.

import 'package:flutter_highlighter/flutter_highlighter.dart';
import 'package:flutter_highlighter/themes/atom-one-dark.dart';
import 'package:flutter_markdown/flutter_markdown.dart';
import 'package:markdown/markdown.dart' as md;
import 'package:google_fonts/google_fonts.dart';

class CodeElementBuilder extends MarkdownElementBuilder {
@override
Widget? visitElementAfter(md.Element element, TextStyle? preferredStyle) {
var language = '';

if (element.attributes['class'] != null) {
  String lg = element.attributes['class'] as String;
  language = lg.substring(9);
}
return SizedBox(
  width:
      MediaQueryData.fromWindow(WidgetsBinding.instance!.window).size.width,
  child: HighlightView(
    // The original code to be highlighted
    element.textContent,

    // Specify language
    // It is recommended to give it a value for performance
    language: language,

    // Specify highlight theme
    // All available themes are listed in `themes` folder
    theme: MediaQueryData.fromWindow(WidgetsBinding.instance!.window)
                .platformBrightness ==
            Brightness.light
        ? atomOneLightTheme
        : atomOneDarkTheme,

    // Specify padding
    padding: const EdgeInsets.all(8),

    // Specify text style
    textStyle: GoogleFonts.robotoMono(),
     ),
   );
  }
}

Next you need to add the Element builder from above into the builders within the Markdown:

 Markdown(
  key: const Key("defaultmarkdownformatter"),
  data: codeText, 
  selectable: true,
  padding: const EdgeInsets.all(10),
  builders: {
    'code': CodeElementBuilder(),
    
  }),

And you should be good to go.

I just wrote an issue :)

Please check Feature: Get Syntax Language when customizing properties syntaxHighlighter #355.

This is content of that issue.

Related Problem

Issue #227 StackOverflow - How to add code syntax highlighter to flutter markdown

Handle the Syntax Language Highlighting.

Possible solution

depends on highlight and of course flutter_markdown.

First, before pass the data to Markdown get a syntax language using RegExp.

Second, marking the language with a identical LANG_MARKER such as L@NG!.

this is an example code.

  String parseSyntaxLanguage(String data) {
    String parsed = data;
    RegExp codeSign = new RegExp(r'`{3} *');
    RegExp pattern = new RegExp(r'`{3} *[\w]+');
    for (RegExpMatch match in pattern.allMatches(this.data)) {
      String lang = match.group(0).split(codeSign)[1]; // get a syntax language
      parsed = parsed.replaceFirst(match.group(0), '```\n$LANG_MARKER$lang$LANG_MARKER');
    } // CAUTION "\n" newline is required!
    return parsed;
  }

Third, Make a syntax highlighter extends SyntaxHighlighter

this is an example code.

import 'package:flutter/material.dart';
import 'package:flutter/painting.dart';
import 'package:flutter_markdown/flutter_markdown.dart';
import 'package:highlight/highlight.dart' show highlight, Node;

class LangSyntaxHighlighter extends SyntaxHighlighter {
  final String language;
  final String _rootKey = 'root';
  final String _defaultLang = 'dart';
  final String _defaultFontFamily = 'monospace';
  final Color _defaultFontColor = Color(0xfffdfeff);
  final Map<String, TextStyle> theme; // User's code theme

  LangSyntaxHighlighter(this.theme);

  @override
  TextSpan format(String source) {
    String lang;
    if (source.startsWith(LANG_MARKER)) {
      int idx = source.indexOf(LANG_MARKER, LANG_MARKER.length);
      lang = source.substring(LANG_MARKER.length, idx);
      source = source.substring(idx + LANG_MARKER.length);
    }
    TextStyle _textStyle = TextStyle(
      fontFamily: this._defaultFontFamily,
      color: this.theme[this._rootKey].color ?? this._defaultFontColor,
    );
    return TextSpan(
      style: _textStyle,
      children: this._convert(highlight
          .parse(source, autoDetection: true, language: lang ?? this._defaultLang)
          .nodes),
    );
  }

  List<TextSpan> _convert(List<Node> nodes) {
    List<TextSpan> spans = [];
    var currentSpans = spans;
    List<List<TextSpan>> stack = [];

    _traverse(Node node) {
      if (node.value != null) {
        currentSpans.add(node.className == null
            ? TextSpan(text: node.value)
            : TextSpan(text: node.value, style: theme[node.className]));
      } else if (node.children != null) {
        List<TextSpan> tmp = [];
        currentSpans.add(TextSpan(children: tmp, style: theme[node.className]));
        stack.add(currentSpans);
        currentSpans = tmp;

        node.children.forEach((n) {
          _traverse(n);
          if (n == node.children.last)
            currentSpans = stack.isEmpty ? spans : stack.removeLast();
        });
      }
    }

    for (var node in nodes) _traverse(node);
    return spans;
  }
}

Last, combine the syntax highlighter and parser.

Widget build(BuildContext context) {
    Future<Widget> parseMarkdown = new Future(() {
      return MarkdownBody(
          data: parseSyntaxLanguage(this.data), // markdown source
          syntaxHighlighter: LangSyntaxHighlighter(),
          styleSheet: MarkdownStyleSheet(
    
         ...

I'm not sure if this is suitable for feature request. However, I hope this issue helps someone :)