We still have the fossil record. It now includes 30+ species that share feathers along with characteristics of therapod dinosaurs.<quoted text>
Then there can be no real evidence to trace how chickens evolved from dinosaurs without DNA evidence.
A chicken would not have evolved from a dinosaur directly. Some early bird evolved from a dinosaur - from something like that bunch above. It then evolved into a bird that evolved in a radiation to other early birds which radiated to other bird and another bird etc. Meanwhile dinosaurs also continued to evolve until they were devastated 65 million years ago.
A chicken is just one of the recent iterations of bird evolution.