This video shows the steps to capture the video from your phone’s camera and then save the video in the download folder of your Android App.

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Complete source code and other details:

package com.programmerworld.videofromcameraapp;

import static android.Manifest.permission.ACCESS_MEDIA_LOCATION;
import static android.Manifest.permission.READ_MEDIA_VIDEO;

import androidx.appcompat.app.AppCompatActivity;
import androidx.core.app.ActivityCompat;
import androidx.core.content.FileProvider;

import android.content.Intent;
import android.content.pm.PackageManager;
import android.net.Uri;
import android.os.Bundle;
import android.os.storage.StorageManager;
import android.os.storage.StorageVolume;
import android.provider.MediaStore;
import android.view.View;

import java.io.File;

public class MainActivity extends AppCompatActivity {
    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main);

        ActivityCompat.requestPermissions(this,
                new String[]{ACCESS_MEDIA_LOCATION, READ_MEDIA_VIDEO},
                PackageManager.PERMISSION_GRANTED);
    }

    public void buttonCaptureVideo(View view){
        StorageManager storageManager = (StorageManager) getSystemService(STORAGE_SERVICE);
        StorageVolume storageVolume = storageManager.getStorageVolumes().get(0); // 0 is for internal storage
        File fileVideo = new File(storageVolume.getDirectory().getPath() +
                "/Download/" + System.currentTimeMillis() + ".mp4");
        Uri uriVideoFile = FileProvider.getUriForFile(this,
                "com.programmerworld.videofromcameraapp.provider",
                fileVideo);
        Intent intentCameraVideo = new Intent(MediaStore.ACTION_VIDEO_CAPTURE);
        intentCameraVideo.putExtra(MediaStore.EXTRA_OUTPUT, uriVideoFile);
        startActivity(intentCameraVideo);
    }
}

<?xml version="1.0" encoding="utf-8"?>
<manifest xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:tools="http://schemas.android.com/tools">

    <uses-permission android:name="android.permission.ACCESS_MEDIA_LOCATION"/>
    <uses-permission android:name="android.permission.READ_MEDIA_VIDEO"/>
    
    <application
        android:allowBackup="true"
        android:dataExtractionRules="@xml/data_extraction_rules"
        android:fullBackupContent="@xml/backup_rules"
        android:icon="@mipmap/ic_launcher"
        android:label="@string/app_name"
        android:roundIcon="@mipmap/ic_launcher_round"
        android:supportsRtl="true"
        android:theme="@style/Theme.VideoFromCameraApp"
        tools:targetApi="31">
        <activity
            android:name=".MainActivity"
            android:exported="true">
            <intent-filter>
                <action android:name="android.intent.action.MAIN" />

                <category android:name="android.intent.category.LAUNCHER" />
            </intent-filter>
        </activity>

        <provider
            android:authorities="com.programmerworld.videofromcameraapp.provider"
            android:name="androidx.core.content.FileProvider"
            android:exported="false"
            android:grantUriPermissions="true">
            <meta-data android:name="android.support.FILE_PROVIDER_PATHS"
                android:resource="@xml/file_paths">
            </meta-data>
        </provider>

    </application>

</manifest>

res/xml/file_paths.xml

<?xml version="1.0" encoding="utf-8"?>
<paths xmlns:android="http://schemas.android.com/apk/res/android">
<external-path
    name="external_files"
    path="."/>
</paths>

<?xml version="1.0" encoding="utf-8"?>
<androidx.constraintlayout.widget.ConstraintLayout xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:app="http://schemas.android.com/apk/res-auto"
    xmlns:tools="http://schemas.android.com/tools"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    tools:context=".MainActivity">

    <Button
        android:id="@+id/button"
        android:layout_width="184dp"
        android:layout_height="98dp"
        android:layout_marginStart="113dp"
        android:layout_marginTop="84dp"
        android:onClick="buttonCaptureVideo"
        android:text="Capture the Video"
        app:layout_constraintStart_toStartOf="parent"
        app:layout_constraintTop_toTopOf="parent" />
</androidx.constraintlayout.widget.ConstraintLayout>

Screenshots: