Only if you can claim them as dependents on your tax return. The IRS only allows you to claim medical expenses for a taxpayer, spouse, or dependent. Please view the IRS link below for more information.

https://www.irs.gov/taxtopics/tc502

What if I am self-employed and claim health insurance premiums, have  child who is 27 but a med student and dependent with a separate policy ... Can I claim her premiums as well?

It depends. 

If you are able to claim your health insurance premiums as an adjustment to income on Schedule 1, you cannot include the dependent's separate policy if it was not issued under your business. 

You are able to deduct the cost of the policy premiums if you itemize deductions and claim medical expenses in excess of 7.5% of your adjusted gross income. 

The premium costs are deductible in that situation.