You could try this: 2 parts, a beam, and a rod constraint.
Part 1 is the anchor at the top. Part 2 is freely moving, attatched via the rod constraint. Use the beam as the visual for the flap, and give it enough segments to look bendy and kinda elastic.
Hello.
You can do this in multiple ways. As I have used one of these to the fullest, but not the other one as I know both of these options can accomplish this.
Hinges (Constraint)
As you can see I have done this previously with two invisible parts next to the flap and using the Hinge constraint by anchoring the invisible parts and leaving the flap unacnhored.
Although they don’t flex like what you have up in the picture. But I do show what I have done below:
Another option is you could use the beam effect, but, i don’t 100% know the properties of it as I haven’t used it much. But it is something else you could try to use, as it does have the bending properties within it if you would rather have your flaps bend when you touch them.
If you need help using the beam effect I would suggest this video:
Conclusion
There is multiple ways to do this. But, I would suggest playing some Airport games, and if they have them you could ask how they made them, but there is more than the two ways I listed to make this possible. Just continue doing some research here on the Devforums and throughout your search engine.