Do you color your wood burned art as well?
I would recommend using a spray varnish first. I use Winsor & Newton All Purpose High Gloss Varnish for my wood burned pieces that I've colored using water color paints/pencils. Perhaps coating it with the spray varnish will help when applying the regular wood varnish.
The spray varnish I use dries crystal clear & depending on how many coats you add, it turns out pretty glossy on the burned areas.
So, spray varnish, then wait for that to fully dry, and add the regular wood varnish
Hope this helps!!