My ESP8266-01 doesn't want to respond to AT command after a successful flash!
The tutorial is to flash SDK 2.0 AT firmware. The AT 2.0.0 firmware is build with RTOS SDK. The 2.0 AT firmware available on Espressif site was build with settings not compatible with esp-01. It is built for 2 MB flash and  communicates over pins 13 and 15.

The latest NonOS SDK AT firmware is 1.7.1 (SDK 3), but it requires 2 MB flash too. It is possible to flash it to 1 MB module with the 2MB-c1 parameter with esptool.py. (The OTA update command will not work.)

GitHub user loboris (Boris Lovosevic) builds customized versions of AT firmware with SDK 3 for all flash sizes. You can download the files from his ESP8266_AT_LoBo GitHub repository. If you can't run his flash.sh utility, then for 1 MB flash you can Flash Download Tool with bin/upgrade/esp8266_AT_1_2.bin file and the right addresses for 1 MB flash: boot_v1.7.bin on 0x0; esp8266_AT_1_2.bin on 0x01000; esp_init_data_default.bin on 0xfc000 and blank.bin on 0x7e000 and 0xfe000.