In this paper, we propose an efficient double-layered flat fiber (DLFF) plasmonic refractive index sensor having high resolution and linearity. Thin gold film is used as surface plasmon resonance (SPR) active material protected by a titanium dioxide layer, both deposited on the upper flat surface of DLFF. The sensor consists of an analyte channel in the central core hole as well as on the top of the fiber. Structural parameters of DLFF and thickness of gold and titanium dioxide layer are analyzed based on the finite element method. The optimized structure is studied based on wavelength and amplitude interrogation techniques in the near-infrared region. Numerical results show average wavelength sensitivity of 12172 nm/RIU with a resolution of 8.21×10-6RIU (refractive index unit) in the highly refractive index (RI) range from 1.445 to 1.490. Further, amplitude sensitivity of this probe is found to be 2910RIU-1 with a resolution of 3.44×10-6RIU, which is the highest among all reported PCF SPR sensors, as per the authors' best knowledge. Compared with traditional photonic crystal fiber, the designed DLFF makes the sensor configuration simple to fabricate as well as a potential candidate for developing biochemical sensors and portable devices.