splicing leaking brake line

Your other option that eliminates the need for flaring altogether is to use a compression union.

Don't use the low pressure type you get at the hardware store only the high pressure ones that you can pick up at an industrial supply store. These fittings in the 1/8" typical brake line size are rated for up to 10,000 psi much much higher than 1500-2000 psi you generate in a brake system.

I have been using these type of compression fittings for 20+ years and have never had a leak or failure.