Video?
Doing chin ups in 3 sets adding 1 rep each 2nd session I do them. Currently at 3 x 9 bodyweight only (I'm 153lb, 5 ft 8, 48yrs). Taking about 8 minutes between sets.
On my first set it absolutely kills my biceps, but I don't feel it in my back at all. Second set seems to go easier than the first. 3rd set I tend to really feel in my back.
Is this normal or should I be trying to get the feeling in my back more right from the start. Trying to concentrate on driving elbows rather than pulling up, but it makes no difference. I do have pretty skinny arms, is it likely because my biceps are comparatively weak?
Video?
Have you tried pronated? As in pullups? It will work your back more without so much help from your biceps.
Also, there are better exercises than chinups for biceps hypertrophy if that's what you want. High rep barbell curls with light weight is one. There are others.
Today's 3rd set of 9. Only made 8 full reps, probably due to my flatmate wanting to play around with bent over rows prior. The rack is low due to my ceiling so rather than jumping up, I have to lower myself and carefully pick up my legs so as to not swing about at the start too much.
YouTube
These are decent chins. Stop worrying about how it feels and get the first set up to 15 reps.