Can I trust a flexible fitting to connect 1 1/2" ABS to existing 1 1/4" pipe, which is sold in the retail outlets for a closed wall bathroom drain? Do these flexible connectors with torque down clamps provide durable connections that will last without leaks?

If you're attempting to connect the trap tail to the wall stubout a better way would be to glue a 1 1/2" compression fitting with a 1 1/2 X1 1/4" nylon gasket,(see image) on the stub out and connect with that. That's how we do it and the compression fitting makes a more ridged connection which means less leaks. Good luck, Tom

Those flexible connectors you speak of are forbidden for use by all of the plumbing codes adopted in the Continental US.

Are you connecting this flex to the wall stub or into a trap?

are you connecting this flex to the wall stub or into a trap?
Doug,
Sounds like he's doing both. Connecting from the wall stubout to the tail of the trap. Cheers, Tom