Is there a tax advantage that I can take to minimize taxes in 2018 if I own a residence in Arkansas and worked the entire year out of Texas? (housing costs, etc) Also paid state income tax in AR, with dual residences.

I donot think so however, your home state is Arkansas and you worked in TX and AZ as a nonresident in the two states and paid AZ tax to Az state government then, since there is no reciprocal agreements between AZ and your home state of Arkansas, you need to pay tax on your AZ source income to AZ as a nonresident of AZ and may claim tax credit on your Arkansas return on the tax paid to AZ.

"AR" = ARKANSAS. Arizona is "AZ". Changes the whole answer I wold surmise.

sorry my bad; confusion then there is no state tax in TX you need to report income that you earned in TX on your home sate of Arkansas tax return.and ONLY WHEN you itemize deductions on Sch A of 1040 on your federal return , you can itemize state tax that you pay to ARKANSAS.