ArrayList Menu Java

You can use the alternate method signature for File.listFiles(FilenameFilter filter) to simplify your code:

File[] files = dir.listFiles(new FilenameFilter() {

    @Override
    public boolean accept(File dir, String name) {
        return name.toLowerCase().endsWith(".txt");
    }
});

And unless you really enjoy writing loops, you don't even need to manually loop over the array to convert it to a List:

List<File> lstRecords = Arrays.asList(files);

Your displayRecord method was pretty close; you just needed to pass the file as an argument and use that instead of a hard-coded filename, and you needed to initialize dis.

Putting it all together:

package com.example.file;

import java.io.BufferedInputStream;
import java.io.DataInputStream;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FilenameFilter;
import java.io.IOException;
import java.util.Arrays;
import java.util.List;

public class FileExample {

    public static List<File> listRecords(File dir) {
        File[] files = dir.listFiles(new FilenameFilter() {

            @Override
            public boolean accept(File dir, String name) {
                return name.toLowerCase().endsWith(".txt");
            }
        });

        return Arrays.asList(files);
    }

    public static void displayRecord(File file) {
        FileInputStream fis = null;
        BufferedInputStream bis = null;
        DataInputStream dis = null;

        try {
            fis = new FileInputStream(file);

            // Here BufferedInputStream is added for fast reading.
            bis = new BufferedInputStream(fis);
            dis = new DataInputStream(bis);

            String line = dis.readLine();
            while (line != null) {

                // this statement reads the line from the file and print it to
                // the console.
                System.out.println(line);
                line = dis.readLine();
            }

            // dispose all the resources after using them.
            fis.close();
            bis.close();
            dis.close();
        } catch (FileNotFoundException e) {
            e.printStackTrace();
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

    /**
     * @param args
     */
    public static void main(String[] args) {

        List<File> lstRecords = listRecords(new File("."));
        for (File record : lstRecords) {
            displayRecord(record);
        }
    }

}

It's also better to use Reader/Writer instead of InputStream/OutputStream if you're working with text files, and you should close your files in the finally block to avoid a potential resource leak.

You'll also notice I didn't explicitly use an ArrayList. In most cases, it's better to program against the interface (in this case, List) as much as possible, and only declare variables using the implementing class when you need to use a method that's only available to that class.

It looks like your sticking point above is the array. If you just need to iterate over the files in a directory, something as simple as the following will do the trick.

import java.io.File;


public class TxtEnumerator {
    public static void main(String[] args) {
        TxtEnumerator te = new TxtEnumerator();
        te.listFiles();
    }

    public void listFiles() {
        String filepath = "." + File.separator + "textDirectory";
        File file = new File(filepath);
        if (file.isDirectory()) {
            for (File f : file.listFiles()) {
                if (f.getName().endsWith(".txt")) {
                    System.out.println(f.getName());
                }
            }
        }
    }
}