That would be the way to go, except: When you upload an image, the submission automatically becomes a "custom image" which will require approval by a moderator, before it can be featured. In contrast, a submission made directly from a built-in/site template can be approved by the software, without human intervention. This is why you'll notice custom submissions taking much longer to feature.
In addition, this "custom image" will not have any template-based tags, since it technically was not created from a template. Similarly, it will not be "linked" or otherwise "associated" with the template that was originally used (if say, you did use a built-in/site template to create the original image). This means that it will not appear on the template's page, among the featured memes created from the template.
Basically, when you save a copy of a submission locally, it becomes just another image. There is no meta-data for ImgFlip to read, upon upload of the image, to tell ImgFlip that the image is a meme created from a particular template. Likewise, there is no retention of the text appearing on the meme, which means, from the ImgFlip perspective, it has no "text." Since the image could be of anything, including offensive language that would normally be disapproved or flagged as NSFW, the image must be reviewed and approved by a moderator, before it can be featured.
As such, we are stuck with having to actually recreate the meme entirely, just before submitting. For memes with extra text boxes, or a non-default arrangement of text boxes, this practice can be very frustrating and tedious. Anyway, hope this helps.