My sister lives in KY. I live in IN and use my address on her tax forms, as I have POA. Her 1099's have IN as her state on Box 13. I plan to file KY taxes. Is that right?

Yes, if your sister is a resident of KY then you would file a KY tax return for her.  If the 1099s are reporting income from a retirement plan, then it would be taxed by her resident state. 

You would only have to file an IN return for her if she has a 1099-MISC with non-employee compensation in Box 7, for work or services she performed in Indiana.  Any such income would be taxable by IN.