After deleting my Yahoo! account, my Flickr account was left intact and I have to contact Yahoo support to get the account removed.
I haven't created Flickr account before Yahoo! account, I initially signed in to Flickr using my Yahoo! email address.
From Yahoo! Help:
You'll lose access to all of your data and content like your emails, email folders, Flickr photos, calendars, Yahoo Fantasy teams and Yahoo Finance portfolios.
Means once you delete your Yahoo! id, you will not be having access for the Flickr.
This question has been asked on the Flickr Help Forum. You can check the forum for more details.
Deleting your Yahoo account initiates a timer. The timer is stopped if you sign in again. After the timer is over, the account will be fully deleted (and all content, too.) For the exact timer period, see https://help.yahoo.com/kb/SLN2044.html