If my understanding is correct, the flex sensor was connected between 5V and GND.
This acted like "short circuit" and should not have burned the AVR, but only the power supply side. If you have a multimeter and some soldering skills it should be possible to fix the board.
Supposing you have an genuine arduino UNO, here is a schematic but it may not be the right version
- Remove the MCU
- Check voltage between GND and XUSB is 5V (if not either your USB port is burned or you have a short on the board or a component)
- Check voltage between GND and USBVCC is 5V (if not, replace the fuse)
- Check voltage between GND and +5V is 5V (if it's still 1.5V as you mentioned, try replacing transistor T1 but I do not understand why it would burn. If it's 5V replace the MCU)
EDIT for Arduino Nano
I did not understand you had a nano board (schematic)
The component "B2" you mention is the diode D1 (MBR0520). It burned because of the short circuit you created and nothing else should be defect. It acted like a fuse. Simply replace it and it should be fine.
If you are VERY CAREFULL not to overload the nano with external circuitery and never bring external 5V you could just remove it and make a little solder bridge (waiting for replacement part)