The reason why your screen is flickering is the constant use of select between the two sheets. In general you can avoid this by using application.screenuptdating = false.
But in the end you should avoid selecting at all - please read How to avoid select.
If you only need the values to be copied, you don't need copy/paste actions. This will increase performance too.
I updated your code - with both scenarios possible (copying values only or - as you did - copying formulas and numberformatting as well - just switch the the comment accordingly
Option Explicit
Private Const MonthRange As String = "C3"
Private Const rowStartReport As Long = 7
Public Sub createMonthlyReport()
ApplicationScreenUpdating = False
Dim wsData As Worksheet
Dim wsReport As Worksheet
Set wsData = Sheet10   'you can set the (code)name in the VBA-Editor - then you wouldn't need this
Set wsReport = Sheet9
Dim Month As String
With wsReport
    Month = wsReport.Range(MonthRange).Value
    wsReport.Cells(rowStartReport, 1).CurrentRegion.ClearContents
End With
    
Dim iRowData As Long, iRowReport As Long
Dim r As Range, rgToCopy As Range, cTarget As Range
For Each r In wsData.UsedRange.Rows
    If r.Cells(1, 1) = Month Then
        Set rgToCopy = r.Cells(, 2).Resize(, 11)    'adjust this to your needs
        Set cTarget = wsReport.Cells(rowStartReport + iRowReport, 1)
        
        'change this to your needs
        'copyValues rgToCopy, cTarget     'this is faster
        copyValuesAndFormats rgToCopy, cTarget   'this copies formulas as well
        
        iRowReport = iRowReport + 1
        
    End If
Next
wsReport.Select
wsReport.Range("A6").Select
Application.ScreenUpdating = True
End Sub
'Two Generic routines to copy values etc.
Private Sub copyValues(rgSource As Range, cTarget As Range)
'this copies values only
With rgSource
    cTarget.Resize(.Rows.Count, .Columns.Count).Value = rgSource.Value
End With
End Sub
Private Sub copyValuesAndFormats(rgSource As Range, cTarget As Range)
'this copies values, formulas and numberformats
rgSource.Copy
cTarget.PasteSpecial xlPasteFormulasAndNumberFormats
End Sub