In my understanding advantage of FBA is that you do not need extensive knowledge about the protein (e.g. Kinetic constants). What you need to know is certainly where the new enzyme would be placed in your network graph: that means, you need to know substrate and product of the reaction the enzyme catalyzes, and to be able to place this reaction in your existing model without creating a gap. In addition you need to define constraints for the flux rates through this enzyme. You can take the SBML file you have and edit it using CellDesigner, your file should be already FBA ready, that means it will contain constraints already. Then you can simply add an enzyme node for the new gene in the correct position. Using copy-paste that should be fairly simple, given you know where your node has to be placed. Also this article might be helpful: http://www.ncbi.nlm.nih.gov/pubmed/20057383

Edit: As Michael Schubert mentions FBA is not supported in COPASI, but maybe openCOBRA which is a Matlab library is suitable for you (Nature Protocols article). Or try FASIMU as a stand-alone application.

I think that the simplest way is to manualy type in the reaction which is catalysed with you desired protein. I use notepad++ just copy-paste the previous gene, properly annotate it (very important) and add a reactants and products in the right stochiometry. It is good that you can also add your own comments (date of introduction, the publications about the gene,...). In my opinion it is faster and more transparent way that doing it in some program.

Martin