What you need is to multi select from the list box. Set the Multi Select property to Simple. Then add this code to a command button.
On Error GoTo Err_Print_ClickErr
Dim vntIndex As Variant
Dim strValue As String
'Check to see if selection has been made.
If lstListBoxName.ListIndex < 0 Then
MsgBox "Please select 1 or more items from the list"
Exit Sub
End If
'Print selection
For Each vntIndex In lstListBoxName.ItemsSelected
strValue = lstListBoxName.ItemData(vntIndex)
DoCmd.OpenReport strValue, acViewNormal
Next
'Error handling
Err_Print_ClickErr:
Select Case Err.number
Case 2501 'cancelled by user or no data for the report
MsgBox "Report cancelled or no data found for the report.", vbInformation, "Information"
' Case Else
' MsgBox "Error " & Err & ": " & Error$, vbInformation, "Print_Click()"
End Select
End Sub