As you can see, there are many styles. The critical areas are the corners. Like the 60 year old galvanized in the link, I much prefer the ole style with tinner's wings on the corners. The style dates back centuries before caulk was commonplace. No reliance on caulk or solder as the metal hides the corner detail from windblown rain and snow. It's ideal for rookies and your work can be less precise.
The devil is in the details. Step flashing needs to be bent less than 90 degrees and pushed into place. The steps must lap each other correctly. The corners must be protected.
The termination flashing on the first piece across the front of the chimney must be cut so it's 1/8" wider than the chimney to ensure a tight fit when that first step flashing rounds the corner. No gaps that way.