My Siri not working in ios8.4

Make sure it is enabled. Go to Settings - General - Siri and move the toggle to the right.

If it is enabled, follow the steps below:

Try to reset your device. This won't delete your data stored on the phone.

• Press and hold the Sleep/Wake button
• Press and hold on the Home button
• Keep holding both buttons until the display turns off and back on with Apple logo on it.

Alternatively, you may go to Settings - General - Reset - Reset All Settings

https://support.apple.com/en-us/HT201559

If this does not help, restore your device to factory settings. Note that this will erase the data from your device.

Take a look this Apple Support article: Use iTunes to restore your iPhone, iPad, or iPod to factory settings - Apple Support.