I don't keep records on my chickens, as I don't incubate their eggs (yet). I do not keep financial records of any type on my birds as I consider them pets, I do however keep records on my quail EGGS.
I record: Who is laying, what do their eggs weigh on hatch day, what day I put the eggs into an incubator, noting when I need to lock down, what they weigh when candled on day 9 (can't tell anything other than developed or not as mine have big dark brown spots on the shells) and whether or not they developed. I note which eggs were not fertilized as I remove them from the incubator. What the eggs weigh on lockdown day, this helps me estimate if they'll have a sufficient air sac, again... can't safely cull anything because the eggs are so dark that I can't tell by candling. I still do the candling process (quickly) hoping that I get better at discerning information from the process, but for me the weighing process gives me more information than candling. (Could be a lack of experience issue). I also record which eggs hatched (and on what day) and which ended up being quitters, failed to pips, failed to thrive, etc. After a hatch is well overdue, the eggs that failed to hatch are eggtopsied to further my understanding of the hatching process and to determine the cause of failure, be it with my flock, the incubator, or myself.