How do you create a database backup of a mysql database in VB.Net?

You can use MySqlBackup.NET, which is an alternative to mysqldump.

Official Website & Documentation > https://github.com/MySqlBackupNET/MySqlBackup.Net

Examples:

Backup a MySql Database

Dim conn As MySqlConnection = New MySqlConnection(constr)
Dim cmd As MySqlCommand = New MySqlCommand
cmd.Connection = conn
conn.Open
Dim mb As MySqlBackup = New MySqlBackup(cmd)
mb.ExportToFile("C:\backup.sql")
conn.Close

Restore a MySql Database

Dim conn As MySqlConnection = New MySqlConnection(constr)
Dim cmd As MySqlCommand = New MySqlCommand
cmd.Connection = conn
conn.Open
Dim mb As MySqlBackup = New MySqlBackup(cmd)
mb.ImportFromFile("C:\backup.sql")
conn.Close