Sounds like you are having the similar problem I had when I first got started on racing quads. I've watched that $99 build by Stu at UAV Futures about a hundred times on YouTube - That's the bug that bit me to get into the hobby! It sounds like you're really close and learned most about droning from YouTube University as I did.
The problem I was having, was that I got a Floureon 250 racer and it worked very nicely out of the box. It also uses the FlySky transmitter/ receiver combo. What happened first was that I updated the firmware to the latest version, then immediately after that, the quad wouldn't respond to the transmitter sticks. I started flashing different versions of firmware with Cleanflight (very similar to Betaflight) and noticed the later versions would not allow the quad to work. They will allow me to bind to the receiver, but not allow me to arm the motors at all. Then I checked in the Receiver portion of Cleanflight, it wasn't showing any responses to stick or switch movements on any channel. Found out I had to switch it to PWM protocol. I did that and I could finally see the channels responding properly. Then I would bind to the receiver again, and still not arm. I tried it for a few nights with no success. So what I did was downgrade the firmware on the FC to a lower version, and the quad responded again. For whatever reasons, the FC would bind but not respond to the transmitter is beyond me.
Check if your receiver responds to transmitter stick movements on Receiver section of Betaflight. Switch FC to PWM protocol if needed. If it still binds to receiver, when you try to arm motors, check if a red LED blinks when you do stick movements. If it does and the quad still doesn't arm, you will have to downgrade firmware to a lower level as I did. Looks like you are using the NAZE32/ 10DOF F3 spracing FC. I have that on my Eachine 250 racer and had the same problem. I did the same thing (downloading firmware level) and now both quads are working fine.
