Is it possible to upload photos directly to my training log using the Instagram app on an iPhone?
I think photos in your log have to be linked from somewhere -- any online photo repository. I don't know how instagram works or where photos are saved, but once you have an online image you can use HTML to link to it. Some applications (Picasa for one) even give you the HTML to copy/paste.
< img src="http://YOUR-URL" >
Flickr is another one giving a HTML. Check if either of them have upload apps.