Before sharing photographs on your blog from Flickr, it's important that Flickr has the correct settings to enable photographs to be shared via a public blog.
Once you have set up your Flickr account click on your profile icon and open "settings".
Next, from the list of tabs across the top of the page, click "Privacy and Permissions".
Below are the settings for my Flickr account which should be fine to replicate for a school account:
Further down the page you may set global update defaults:
In the above settings, the only change a school might make is to change the "Content filters" search settings to "Safesearch: On", although since children won't have direct access to the Flickr account it doesn't really make a difference.
The default upload settings apply when you are uploading images directly from your browser to Flickr. If you are using the Flickr App you can set the default upload to private. Alternatively, you can use the Auto Uploadr which automatically uploads all images on your device to Flickr whenever you open the app, but they always default to Private. If you set uploads from the app to default as private you most go to your Flickr Camera Roll, select the uploaded pictures and change them from private to public before they can appear on your blog.