How to create multiple instance of a usercontrol through a loop in MVVM

Use an ObservableCollection holding Models or ViewModels of the data to be displayed in the multiple UserControls. Then in the XAML file, use an ItemsControl (wrapped inside a ScrollViewer control) or ListBox and set the DataTemple with the UserControl.

UPDATE: Here is a working example for you as requested...

Models and ViewModels may have properties that can change. Here is a base class that works with the INotifyPropertyChanged binding interface:

public abstract class ObservableBase : INotifyPropertyChanged
{
    public void Set<TValue>(ref TValue field, TValue newValue, [CallerMemberName] string propertyName = "")
    {
        if (EqualityComparer<TValue>.Default.Equals(field, default(TValue)) || !field.Equals(newValue))
        {
            field = newValue;
            PropertyChanged?.Invoke(this, new PropertyChangedEventArgs(propertyName));
        }
    }

    public event PropertyChangedEventHandler PropertyChanged;
}

NOTE: This is NOT required for this sample app but here for thoroughness for the Binding system.

For our sample app, we need a data model to bind each item in the ObservableCollection in the MainViewModel class:

public class PersonModel : ObservableBase
{
    private string name;
    public string Name
    {
        get { return name; }
        set { Set(ref name, value); }
    }

    private int age;
    public int Age
    {
        get { return age; }
        set { Set(ref age, value); }
    }
}

Now we can define our MainViewModel that will hold our collection of objects to be displayed in the MainWindow UI

public class MainViewModel
{
    public MainViewModel()
    {
        Mock();
    }

    public ObservableCollection<PersonModel> Persons { get; set; }
        = new ObservableCollection<PersonModel>();

    private Random rand = new Random();

    private void Mock()
    {
        for (int i = 0; i < 10; i++)
        {
            Persons.Add(new PersonModel
            {
                Name = string.Format("Person {0}", i),
                Age = rand.Next(20, 50)
            });
        }
    }
}

Now we define our item template in the UserControl as required in this question asked:

<UserControl
    x:Class="ItemsControlSample.PersonUserControl"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml">

    <Grid>
        <Grid.ColumnDefinitions>
            <ColumnDefinition/>
            <ColumnDefinition Width="Auto"/>
        </Grid.ColumnDefinitions>
        <TextBlock Text="{Binding Name}" Margin="10 3"/>
        <TextBlock Text="{Binding Age}" Margin="10 3" Grid.Column="1"/>
    </Grid>

</UserControl>

Lastly, we are now ready to define our MainWindow UI view for the user:

<Window
    x:Class="ItemsControlSample.MainWindow"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"

    mc:Ignorable="d"
    xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
    xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"

    xmlns:local="clr-namespace:ItemsControlSample"

    Title="Basic ObservableCollection binding example"
    WindowStartupLocation="CenterScreen" Height="400" Width="360">

    <Window.DataContext>
        <local:MainViewModel/>
    </Window.DataContext>

    <Grid>
        <Grid.ColumnDefinitions>
            <ColumnDefinition/>
            <ColumnDefinition/>
        </Grid.ColumnDefinitions>
        <Grid.RowDefinitions>
            <RowDefinition Height="Auto"/>
            <RowDefinition />
            <RowDefinition Height="Auto"/>
        </Grid.RowDefinitions>

        <Grid.Resources>
            <DataTemplate DataType="{x:Type local:PersonModel}">
                <local:PersonUserControl/>
            </DataTemplate>
        </Grid.Resources>

        <TextBlock Text="ItemsControl Example" FontWeight="Bold" Margin="4 10"/>
        <Border BorderThickness="1" BorderBrush="Silver" Margin="4" Grid.Row="1">
            <ScrollViewer HorizontalScrollBarVisibility="Hidden"
                          VerticalScrollBarVisibility="Auto">
                <ItemsControl ItemsSource="{Binding Persons}"/>
            </ScrollViewer>
        </Border>

        <TextBlock Text="ListBox Example" FontWeight="Bold" Margin="4 10" Grid.Column="1"/>
        <ListBox ItemsSource="{Binding Persons}" Margin="4" Grid.Row="1" Grid.Column="1">
            <ListBox.ItemContainerStyle>
                <Style TargetType="ListBoxItem">
                    <Setter Property="HorizontalContentAlignment" Value="Stretch"/>
                </Style>
            </ListBox.ItemContainerStyle>
        </ListBox>
    </Grid>

</Window>

The sample app shows how to display a list of Models contained in an ObservableCollection in the bound ViewModel using both an ItemsControl and a ListBox control using the MVVM Pattern and the WPF Binding system.