Some days back Flickr has released a free app for iphone available on apple store, you can search for the flickr app on apple store and install this free application. This official application from flickr will allow you to upload images on your iphone to your flickr profile directly.
Note: In order to start uploading the images from iphone to flickr, you will need to authorize the app on your flickr account, but don’t worry as you don’t need use your computer to do this, you can do it from iphone directly.
Here is the step by step procedure on how to use this flickr app to upload images online from iphone
After installing you will see the following screen when you first time open the applications
Click Sign In, to approve to the app on your account, it will launch safari browser on iPhone to get approved.
To start uploading images, click the camera icon on the right top and select the image from camera directly or upload any image from iphone photo library.
after uploading you can change the settings like viewing permissions
I hope this tutorial explained is understandable and easy to implement for those who have asked for it.