Yes, an adult child may purchase life insurance on each parent.
Since you are related as parent and child, there is Insurable Interest between you and your parents, which means you can purchase life insurance on your parents.
If you are looking for life insurance to provide money to pay for their final expenses, including burial and funeral costs, you may want to consider a funeral insurance plans.
Funeral life insurance offers plans with guaranteed approval, or simplified issue policies which make it easy for you to apply online and purchase life insurance for your parents.
Funeral life insurance has no medical exam required, but their may be a few Yes/No health questions for you to answer about your parents' health.
In addiiton, there are guaranteed issue life insurance plans for seniors that offer guaranteed acceptance for people ages 45 to 75, or older, depending on the insurance company age requirements.