You
don't need application number for filling the form, but you need your parents UCI, if you can't find it, just write an explanation letter and attach it with your application package
If your parents have dealt with CIC/ IRCC in the past. There should be UCI on the letters or correspondence with IRCC for visitor or super visa, if you don't have those letters, the visa stamp on your parents passport will also carry UCI#
I have also heard that the visa stamps before year 2010 didn't carry UCI# (
NOT A CONFIRMED INFORMATION THOUGH)