+1 your rim tape looks perfect.

Are you getting small punctures, or blowouts?

When you mount the tire, before inflating, check both sides very carefully all the way around the rim to be sure you haven't pinched the tube.

Finally, everyone flats at least occasionally. Get yourself a good frame pump or CO2 kit and carry a spare tube and levers! The old adage is carry that stuff, or only ride as far as you'd like to walk home.

Nice looking bike!

btw I once had a crazy run of bad luck like you're having, and it seemed to be the particular marriage of rim and tire I was using. I can't explain why, but in my case, switching to Gatorskins cured it. If all else fails you might try a different tire and see what happens.