I don't think it's not so straightforward, with the inject dsDNA->anti-dsDNA antibodies idea
There is free DNA in the blood all the time, coming from your own dead cells, which is indeed now used for liquid biopsy and sequencing.
This must mean that developing the mere presence of free DNA does not lead automatically to anti-dsDNA antibodies.
It would probably depend (among many other things) on the concentration. And for a DNA vaccine I imagine that such concentration is quite low. Indeed, you would rely on the subsequent expression of protein at high levels from that DNA.
I would be more "worried" about the immune cells mounting a response against your own cells (transfected with the DNA) and developing an auto-immune disease in the process. The survival of plasmacells depends on the inflammatory environment and their stimulation with the antigen, this leads to some tolerance for cross-reactive and auto-antibodies during infections.
In the case of DNA vaccine the non-self antigen is being produced and presented (on MHC-I complexes) by self-cells, so I can imagine that there will be a certain degree of cross-fire.
Once the transfected cells are cleared out, the cross-reactive antibodies should also clear out, but there might be some exceptions to this.