Though you can't use flash, it is still possilbe to add, delete, and edit your photos on Flickr. It's just a bit awkward.
Using a Flickr app like FlickStacker you can upload and download photos to Flickr, with reasonable control over your tags, albums, etc. When you do this the photos end up in the Photos app on the iPad. This turns out to be a good thing, since most image editing apps have the option to load and save to the Photo app's gallery as well.
So, you download your picture from Flickr, using your app of choice. It ends up in the default photo app on the iPad. You open your favorite image editor [there are dozens of choices] and import the picture from Photos. Edit, export back to Photos, and then use your Flickr app to upload it again.
See, simply convoluted. And you have to learn the quirks and methods of each app you chose, instead of just one web site.
It does have some advantages though. You are not limited to Flickr's editor. You can pick the one you want, or pick a dozen of the cheaper one trick ponies.
Also, while editing the photos you won't need to be connected to the internet. Just when you need to upload or download them. So you can grab a bunch you want and work on them any time you've got the iPad handy.