Lot's of opinions here. Many valid points have been made.
In my opinion, synthetic oil of the correct viscosity will reduce friction and extend engine life. I switched my flathead to synthetic on the last oil change with the idea in mind that this engine should last the rest of my life without rebuilding. PERHAPS there's more leakage past seals, but, in my case, it would measured in drops per month.
I last replaced the oil 9 months ago, have driven 1000 miles since, have lost no more than 1/4 quart in that time, if that, so that's a win. In fact, it's better than than my last car with a 383 stroker Chevy crate motor which used a quart every 3000 miles.
All of the oils today are better than anything available in the flathead era. The only thing I might avoid is an oil with no additives, which would actually be pretty hard to find.
So, review the opinions and make your choice. It's likely that any oil of the right viscosity rated for modern cars will be a safe choice.