Removing the galvanized coating by burning will produce yellow fumes of zinc oxyde that are poisonous. It's better to remove them by means of a grinding wheel, very carefully of course, so as not to remove, or remove as little as possible, the base metal.
The weld must be done before you apply the zinc rich primer, also called "cold galvanizing".
That's how I did back in my days of erector engineer.
Giovanni S. Crisi
Sao Paulo - Brazil

A client asked me to weld several hot dipped gavanized plates to show an engineer that there were no problems associated with welding through galvanized coatings. I welded several samples using E6010 and several others with E7018 without removing the hot dip galvanize. Each sample was then cut, polished, and etched with acid. Each macroetched sample had what appeared to be zinc along the grain boundaries in the weld adjacent to the toes of the fillet weld. Some of the samples were then fractured. In each case, the galvanized samples appeared to be more "brittle" when compared to samples that were welded without hot dip galvanize coatings.

I wouldn't say the samples were welded and tested "scientifically", but it did show my client that it was well worth the effort to remove the galvanize coating before welding.

Zinc oxide fumes are generated if the welder welds through the zinc coating or if the coating is "burned off" using a torch. The fumes can result in metal fume fever, i.e., a fever, with chills and sore aching joints,if a respirator is not used.

I hope this helps.