I'm really happy you attached the video for this! I can actually see a few things other than your arm that need to be changed to help you:
- the most important thing is that your roundoff needs to be improved (legs coming together faster, more push off of your hands with a faster snap down) so that you can land the roundoff with your chest up, arms at your ears and with knees behind or in line with toes when absorbing (see 0.04)
- although the roundoff is leading to this, the main problem with your actual handspring is how you're getting into it - you should be seated in the way I described above, but with your knees in front of your toes as they are here it causes your chest and arms to reach back to the ground earlier than they should (meaning you don't actually jump or get any height into the handspring, see 0.05). Without height, your arms literally do not have time to be in the proper position to support how your weight is distributed
- unrelated to those problems if you go to a later point in 0.05 you see that even before your hand is on the floor you begin to move them together. This will likely just take repetition.
- the last problem is the body positions in the back handspring. You should jump back into a tight open body position (legs together and straight, arms close to ears and pushed as far back as possible, and hips up). When your hands hit the floor you should begin to snap into a hollow body position through your hips and push through your shoulders to block off the ground. You are closing your shoulders (likely due to your hand placement) and then just piking your legs down (see the end of 0.05)
I know this seems like a lot in response to an arm bending question, but I believe these are all things that will help fix your arm but will also help you when you want to move on to multiple handsprings and eventually tucks etc. If you need any drills related to these tips just ask!