How does one ask family to see if they’d be willing to donate a kidney to another family member?

i would use an open letter to the family, with no expectations, and stating exactly that. no response required.

I don't see where asking individually would encourage any one of them to help. OTOH you could send a letter out to the whole family mentioning your brothers condition and asking if anyone knows of someone that would be willing to donate.

Sadly too many die while waiting on the transplant list. A friends daughter recently passed while waiting. She had been on the list for ten years after her first donated kidney failed several years after she received it.

If you aren't designated as a donor on your drivers license...make sure you sign up.

And be careful out there when you are riding your 'donorcycle'...

I never actually had to ask. As soon as a doctor diagnosed me with kidney failure and said I needed a transplant, my sister volunteered immediately.

You can't really ask people for body parts

Nothing to lose, except the answer no. Just ask if it would be possible to consider donating. No hard feelings if not willing or able.

I guess the same "everyone" will know that the patient needs a transplant and is waiting for a donor. Here it would be common practice for the doctors to advise the patients close family of the need for a donor and for interested parties to be screened as a match. From there its up to someone to put their hands up.

I don't think you can. My wife's grandma died of kidney failure because her identical twin sister wouldn't give her a kidney.

there was a person that had a truck with it written on the back window and a number to call, don't stop at family

I imagine so.
Unless it's a religious thing.

You would think someone would step up without asking, but blood kin can be some of the most selfish assholes we all know.