I'm not sure what you're asking exactly.. Do you mean that you don't want to invest the effort in clicking on the image button, or do you mean that you don't know how to put pictures from Flickr onto this forum?
Option 1: In Flickr, click on the all sizes icon for a picture of interest. Select the size you want, copy the URL out of the "Grab the photo's URL" box. Click on the image insert icon on MR (yellow "picture" with mountains and the sun) and paste it in the pop-up.
Option 2: You can take that URL and make the image tags yourself: [ IMG ] the URL [ / URL ] (take out the spaces).
If you want Flickr to show you a tag box that has the image URL inside the IMG tags, *shrug* I'm not sure how to do that.
if you use flock (web browser) you can upload images to flickr using the program and it automatically generates bb code (what this, and many other forums use) and html code.
For what it's worth, clicking on the picture icon above the textbox on the forum is completely different than uploading the attachment to MR. All that button does is create the IMG tags for you.