I am 66 years old and I have 2 sons who are irresponsible. I worry who will take care of my finances if I should become incapacitated?

You should also think about POA, will, and end of life directives. This is a very good question. My wife and I have no kids and are thinking about assigning POA to a niece and nephew as secondary POA. You can also hire medical advocates to see to your elder care and end of life wishes.

Do you have any brothers, sisters, nieces, nephews and/or cousins you trust? If not family, what about a close friend?

If you do follow one of these routes, I would consider preparing a letter or Affidavit supporting your decision, even addressing the son's irresponsibility so there's no family contest if anything does happen.

All my incoming checks are on auto deposit, all my bills are on auto pay.
I have a great kennel to take care of my pets.
I figure that covers a pretty long hospital stay.
Many people have more complicated financial pictures.

One thing you can do is try make your finances as uncomplicated as possible. Consolidate any mutual funds/stocks under one investment planner, don't have accounts at multiple banks, and downsize and invest any money received from that yourself so they won't have to look after that later. One thing I did for my mother is invest a portion of her money in an insurance based GIC, she is able to withdraw funds monthly, it earns interest and the money pays out to her beneficiaries without passing through probate. But I don't know how that would play out for medicaid for you all down in the USA.

first thing i'd do is disinherit them.
and, perhaps, some long term care insurance? I think that is still possible.

Or find a friend you trust. I'm single, no kids, so at some point, I'll have to find someone to help in that area. I'm not nearly there yet (at 65)...but I'm working on having younger friends I can turn to.

I would hire an accountant or CPA to take care of your finances since you feel your sons wouldn't make good financial decision for you. The accountant/CPA can advise.