The thing is that we do not have frontend filter (checkbox) to filter the post by current user.
Maybe, what if you create a new page "My Own Posts" and create another view "view-my-own-post" and with this view you add the author filter as shown above and add this view to the page "My Own Posts".
Then add link to that page ("My Own Posts") instead of checkbox and when you click on this it will redirect you to that page that will display the own post.
if the above option does not look good, then the another option would be, we can add a checkbox to your current view and submit button.
And we will use the wpv_filter_query to hook the author filter dynamically.
Please let me know with what option you would like to go with and if you want to go with the checkbox option then I will require admin access details and to what view you want to add checkbox (my-own) filter and to what page you added your current view.
*** Please make a FULL BACKUP of your database and website.***
I would also eventually need to request temporary access (WP-Admin to your site. Preferably to a test site where the problem has been replicated if possible in order to be of better help and check if some configurations might need to be changed.
I have set the next reply to private which means only you and I have access to it.