I did not run into an error for this line of code

wbk1.Sheets("Sheet1").Range("$A:$K").Copy wbk3.Sheets("Copy").Range("$A:$K") 'Change the Sheet name and data range accordingly
However, I did have an issue with this line
wbk2.Sheets("Sheet1").Range("$A2:$K").Copy wbk3.Sheets("Copy").Range("A2" & Rows.Count).End(xlUp).Offset(1, 0) 'Change the Sheet name and data range accordingly
Please retry the full code below. Remember to pay attention to the notes in the code
Sub CombineWBks()
  Dim strFirstFile, strSecondFile, strThirdFile, dialogTitle As String
  Dim wbk1, wbk2, wbk3 As Workbook
  Dim fileDialog As fileDialog

'Speeding up the macro
  Application.ScreenUpdating = False
  EventState = Application.EnableEvents
  Application.EnableEvents = False
  CalcState = Application.Calculation
  Application.Calculation = xlCalculationManual
  PageBreakState = ActiveSheet.DisplayPageBreaks
  ActiveSheet.DisplayPageBreaks = False
  Application.DisplayAlerts = False

  dialogTitle = "Navigate to and select required file."
   Set fileDialog = Application.fileDialog(msoFileDialogFilePicker)

   With fileDialog
    .InitialFileName = "C:\_ExcelForum\CombineWorkbooks\" 'CHANGE THE INITIAL FILE LOCATION
   '.InitialFileName = ThisWorkbook.Path & "\" 'Alternative to previous line
    .AllowMultiSelect = True
    .Filters.Clear
    .Title = dialogTitle
   
   If .Show = False Then
    MsgBox "File not selected to import. Process Terminated"
Exit Sub
   End If
   
  strFirstFile = .SelectedItems(1)
  strSecondFile = .SelectedItems(2)
   End With

  strThirdFile = "C:\_ExcelForum\CombineWorkbooks\Test.xlsm"
  
  Set wbk1 = Workbooks.Open(Filename:=strFirstFile)
  Set wbk2 = Workbooks.Open(Filename:=strSecondFile)
  Set wbk3 = Workbooks.Open(strThirdFile)

'COPY PROCESS BEGINS
      wbk1.Sheets("Sheet1").Range("$A:$K").Copy wbk3.Sheets("Copy").Range("$A:$K") 'CHANGE THE SHEET NAME & DATA RANGE ACCORDINGLY
      wbk1.Close

      wbk2.Sheets("Sheet1").Range("A2:K500000").Copy wbk3.Sheets("Copy").Range("A" & Rows.Count).End(xlUp).Offset(1, 0) 'CHANGE SHEET NAMES

      wbk2.Close
      wbk3.Save
      wbk3.Close

'Restoring Speeding up the macro
  Application.ScreenUpdating = True
  Application.EnableEvents = True
  Application.Calculation = xlCalculationAuto
  ActiveSheet.DisplayPageBreaks = True

End Sub