I think you can't simply reuse the rpi3 env, but you can use it as a template to how to get this working for the beaglebone black. So you would need to get a cross compiler and then extract the sysroot to compile Qt on your own. After you got Qt compiled, you will also need to make some changes similar to these [1] But I think the hardest part might be to get Qt compiled for the beaglebone black, because the info I found online seems to be a bit outdated.

https://github.com/therecipe/qt/pull/226/files