I'm no stranger to using router templates for flush trimming, but I white-knuckled it with these chair parts.  The long curves meant the grain direction could change pretty dramatically over the length of the cut.   Even with the bottom/top bearings spiral bit and switching between bottom/top template routing to maintain downhill cutting, I still had many catches.  End grain is always a challenge, and traversing an abrupt curve on end grain while keeping the bearing in contact the template is doubly challenging.  I had a number of scary catches.

No pics, but I started by tracing the template shapes onto the blanks and rough cutting them out on the bandsaw.   I tried to keep the cut proud by 1/16" or so.

The curve of the sectioned back stile had areas that were semi-end grain.  It got a little grabby when flush cutting in places, but it wasn't too bad.

Flush trimming the arm and seat components went pretty smoothly, even traversing the narrow ends went pretty well.   I took those ends slow, using one hand closest to the bit to press the part down against the table and act as a pivot point while using the outboard hand to lever the work slowly around the tip.  If you can keep the bearing tight on the template and move really slowly, you can minimize any catches.

Where I started having real problems was flush trimming these narrow pieces that will build-up the arm width (template not shown).

I wasn't even attempting to trim around the tip of these parts.   I was just trimming the bulk of the long edges when I got this bad catch.  This massacre could have been avoided if I had just looked underneath to check the grain direction.  At this point, I had switched to a different spiral bit with a bearing only on the end, which I did because I wanted its longer cutting length.   Bad move.  For the rest of these parts, I made some very light (controlled) climb cuts along the length to remove the bulk of the excess, followed by a regular cut to clean it up.  The climb cuts are harder to control, but have less tear-out.

Fortunately, I was able to press that tear-out back down with a couple clamps and wick-in some low viscosity CA glue to lock the fibers back in place.

I'll clean-up the ends at the oscillating sander where I didn't want to risk flush trim routing.

That's all the squared-off shaping of the long parts.

The remaining parts (primarily the stretchers) I'll be able to cut on the CNC and avoid the scary router table.