Can your heirs avoid probate if you put another person on your checking or brokerage account?
Yes. Probate may be avoided as to the accounts in question by putting another person on the account. Other assets, such as real estate, may go to probate however. This answer applies only to the accounts mentioned.
I caution you not to do this, however. If you put another person on your account, they become a joint owner. This means they can access your property. Worse yet, their creditors can access your property if they get into financial difficulty or get divorced. Your account could be at risk.
It is better to set up a pay on death account or otherwise name a beneficiary for the account to take place upon your death. While this is better than a joint account, there are still potential problems. What if your named beneficiary dies before you? Your account will be back in probate. As account values rise and fall, you may end up with a smaller gift to the beneficiary than you wished.
Without knowing the value of the accounts in question and whether or not there are other assets to consider, it is difficult to give specific personal advice. For specific advice, you should consult a local licensed attorney. My usual recommendation is to set up a revocable living trust in order to avoid probate, however if the estate is small, that may not be needed.