Redmi Note 4 is a flagship phone from the Mi Group and a value for money device. There's no doubt that it is indeed one of the best choices you could have made.
Coming to your last question first, about its availability in Flash sales. Yes, you can get Redmi Note 4 through Flash Sales from the following places:
i) Redmi note 4 is been made available on Flipkart through their Android app or through Chrome extension. The next sale is going to be on 05th April at 12 noon and this phone will be exclusively available on Flipkart and Mi.com/in.
ii) Redmi has been rated by Amazon as an exclusive mobile. It is rumoured that Redmi 4, is going to be launched on 20th March. It might be announced as Redmi 4A flash sale.
Coming to your other query about some other good phones under the same price range, I have listed them down in the sequence of their customer rating, and of course a little bit of my own opinion.
1. Honor 6X
It is a phone with 12MP+2MP dual lens primary camera that is equipped with auto focus and FF. The front facing camera is of 8MP with PDAF Focusing feature enabled. The display is of 13.97 centimeters (5.5-inch) with LCD LTPS/a-si capacitive touchscreen having 1920 x 1080 pixels resolution with 403 ppi pixel density and 16M color support.
The phone runs on Android EMUI4.1 v 6.0.1 Marshmallow operating system supported by a 2.1GHz + 1.7GHz Kirin 655 octa core processor. You get 3GB RAM, 32GB internal memory which can be expanded up to 128GB. It has dual SIM slots both with 4G and VoLte support.
The device is powered by a 3340mAH lithium-polymer battery that gives a talk-time of 23 hours and standby time of 650 hours.
2. Moto G Plus
Starting with its Cameras, the phone brings you a 16 MP primary camera which has features like PDAF and professional mode, laser focus, and a 5 MP front camera with wide angle and display flash. Other features include Finger print reader, 5.5-inch full HD display with 1920 x 1080 pixels resolution and 401 ppi pixel density protected by a Corning Gorilla Glass 3.
The phone works on Android v6.0.1 Marshmallow OS which is upgradable to Android v7.0 Nougat and even with Motorola mobile computing system that gets support from a 1.5 GHz MSM8952 Qualcomm Snapdragon 617 octa-core processor with 550 MHz Adreno 405 GPU. Storage includes 2GB RAM, 16GB internal memory which gets expanded up to 128GB. It has dual micro-SIM and dual-standby suppporting 4G and 3G. Its 3000 mAh battery will give you all day work with special TurboPower charging that takes only 6 hours of power in only 15 min of charging.
3. Coolpad Cool 1
This is one of my favourite brands. This phone is based on Android v6.0 Marshmallow operating system with 1.8GHz Qualcomm Snapdragon 652 Octa core processor. It has a storage capacity of 4GB RAM and 32GB internal memory. The phone sports a 13MP Primary Dual-Camera with Dual 6P lens, F2.0 and an 8MP Front facing camera. The display is consisting of 5.5inch IPS capacitive touchscreen with 1920 x 1080 pixels resolution and 403 pixel density with EUI 5.8. This too has dual SIM slots and dual-standby both supporting 4G. The phone gets its power from a 4000mAH lithium-polymer battery that can give a talk-time of 12 hours and standby time of 450 hours.
4. HTC Desire 728
With Android operating system v5.1.1 (Lollipop), 3GB RAM and 32GB internal memory, this phone is another value for money device with 13MP primary camera and 5MP front facing camera. The Display is of standard 5.5 inch with 720 x 1280 pixels resolution. The phone is powered by a 2800 mAh Li-Po battery with which you get a talk-time of 26hours and stand by upto 496hours.
5. Vivo V1Max
This is yet another good phone working on Android v5.0 (Lollipop) operating system. It comes with 2GB RAM and 16GB internal memory. The Cameras include 13MP primary camera with auto focus and 5MP front facing camera. This device too has a 5.5 inch Display with 720 x 1280 pixels resolution. The phone earns you talk-time of 14hours and standby time upto 410 hours from its 2720 mAh battery.