It can't be done as you have described. Simple as that... however, you can create a transparent PNG from form posted data and overlay it over the FLV. FFMPEG kind of sucks for that purpose but
sothink has a way better encoder you can use... it's $600 to buy but it's worth every penny. It can also generate an swf player on the fly that contains the flv and I am fairly positive that this encoder can do it in under a minute. The trick will be dynamically sizing the text to fit into the fansign box and positioning the png over the flv. It shouldn't be super difficult since your flv is always the same size and you can put limits on the amount of text that can be used (the name).