Since (and included) 1.14, when chicken dies burnt with 1 tick of lava doesn't throw coocked (nor raw) drop, but they throw feather.

I've done some testing in my world (see image or download link) and I get LESS than 1% drop rate of coocked chicken when killing them with that system.

I've noticed that they die instant, in 1.13.2 they took three hits after lava disappeared with flames. I checked and you didn't change the life nor the lava damage (or didn't notice).

It works fine before 1.14, and, in fact, it's the main design of most chicken farms... As you will expect, having 24max mobs in a block and 1% drop makes it so inneficient that it is not worth it to build it.

I attached 3 imaged of the process, killing 20 chicken with the system and only getting 1 chicken (somteimes it takes much more to get one).

I also attached the world where I test it (of course where I noticed it was in another one in survival). The system is at coordinates 0 ~ 0.