how to create a row of scrollable text boxes or widgets in flutter inside a ListView?

I think this is straightforward as long as you put a container of fixed height on your horizontal ListView. But maybe I'm not understanding your question. Please post your code and the error message you're getting if this doesn't work.

import 'package:flutter/material.dart';
import 'package:flutter/gestures.dart';
import 'dart:collection';

void main() {
  runApp(new MaterialApp(home: new DemoApp()));
}

class DemoApp extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return new Scaffold(
      appBar: new AppBar(title: new Text('Nested ListView Example')),
      body: new Center(
        child: new ListView(
          children: <Widget>[
            new Container(
              height: 80.0,
              child: new ListView(
                scrollDirection: Axis.horizontal,
                children: new List.generate(10, (int index) {
                  return new Card(
                    color: Colors.blue[index * 100],
                    child: new Container(
                      width: 50.0,
                      height: 50.0,
                      child: new Text("$index"),
                    ),
                  );
                }),
              ),
            ),
          ],
        ),
      ),
    );
  }
}

I have done this to make my Row widget scrollable:

Text("Debilidades",
    style: TextStyle(fontWeight: FontWeight.bold)),
SingleChildScrollView(
  scrollDirection: Axis.horizontal,
  padding: EdgeInsets.fromLTRB(10.0, 0.0, 10.0, 0.0),
  child: Row(
      mainAxisAlignment: MainAxisAlignment.spaceEvenly,
      children: pokemon.weaknesses == null
          ? <Widget>[
              Text(
                "No tiene debilidades",
                style: TextStyle(color: Colors.grey),
              )
            ]
          : pokemon.weaknesses
              .map((weakness) => FilterChip(
                  backgroundColor: Colors.red,
                  label: Text(
                    weakness,
                    style: TextStyle(color: Colors.white),
                  ),

                  onSelected: (b) {}))
              .toList()),
),

For a row/column to scroll you can simply use the SingleChildScrollView feature and mention the direction as required.

SingleChildScrollView(
    scrollDirection: Axis.horizontal,
    child: Row(
        children: [
            //provide all the things u want to horizontally scroll here
        ]
    ),
);