I wants to use cell button CR2032 for Power up Arduino R3 board.
Specification of Cell button is 3 v 10 ma & required For Uno R3 is 5 V 50ma.
So for Voltage amplification i already used series of two button cell which give me 5 V but for Current amplification i wants to use Current amplifier.
You cannot use the R3 board because it has a rather inefficient linear regulator.
To run on a 3 volt coin cell you could build your own Arduino (minus all the voltage reg stuff) and feed 3 volt in directly, although you will need to use a different bootloader and run it at 8MHz, or keep with 16MHz and run in 6 volt. A good quality electrolyte cap will help with short term current requirements.
With careful use of sleep mode you can get very low power consumption, for example I have built a remote sensor using AA batteries that has been running for over 2 years.
The other issue of course is what the Arduino is doing and how much current that needs.
Adding batteries in series increases voltage.
Adding batteries in parallel increases amperage (Ah or mAh).
If indeed the battery specs are 3V/10mAh then you would need 5 pairs of CR2032 (2 each in series) connected in parallel to get 6V/50mAh. Of course, this will cancel any desire for a very small device.
Note that after a little research, I read that the minimum mAh for CR2032 is usually 150, so 2 in series should be more than enough.
Someone here may know more about the numbers than I.
To run common MCUs from a coin cell battery for a reasonable amount of time you need to use some form of sleep mode a lot as well as turn off any other power hungry circuitry for most of time. Arduino Uno is NOT suitable for such task unless you remove nearly everything from it. IMHO the other way is much better - start with a bare ATMega (the brain of Arduino Uno) and add components you are missing from Arduino Uno. This way you can get to VERY low current consumption - in order of single micro-amperes of average current! It is not so hard but you need a lot of knowledge. I was able to do something like that about a year after discovering electronics as a hobby.
Keep in mind that if you disconnect the arduino VReg and LED, then you can reduce mAh = 3.5mA active / <1mA Sleep
Of course, you are using the RAW Pin, and Disconnecting the LED and the VReg ...
ATmega328P Pro Mini Version PWR Source State 5.0 V @ 16 MHz 3.3 V @ 8 MHz
Unmodified RAW Pin ACT 19.9 mA 4.74 mA
Unmodified RAW Pin PDS 3.14 mA 0.90 mA
No Power LED RAW Pin ACT 16.9 mA 3.90 mA
No Power LED RAW Pin PDS 0.0232 mA 0.0541 mA
No Power LED, no Regulator VCC Pin ACT 12.7 mA 3.58 mA
No Power LED, no Regulator VCC Pin PDS 0.0058 mA 0.0045 mA
ACT - Active Mode
PDS - Dower-Down Sleep with Watchdog Timer enabled