So, as @jooja puts it in the comments - not all oeprations are convolutions, nor does convolutions sum up that nicely.
Seen your comments, this is not actually what you are in need for - this specific requiste of "finding the equivalente convolution" could be the research work of a Computer Scientist doing Image Processing theoretical research.
Since you are simply trying to automate modifications to images, based on things you have done using the UI, you should resort to scripting. I do recomend using Python of the two pre-installed programming languages (the other, script-fu, being Scheme) - and simply make calls to the functions available that are equivalent to any actions taken on the UI.
GIMP can perform through scripting nearly 100% of the operations it can do via manual image editing - and a script can be run without GIMP ever opening a GUI Window - since you commented you'd want that behavior.
To get started, check the filters menu under python->console and use the browse button to see the available methods. To get started type image = gimp.image_list() to get a reference to an open image. Further questions on scripting should be on stackoverflow.com –