Hooking up two voltage regulators for more power?
To give an official answer:

No, it's not okay. With today's production you can give it a try in a small experiment, in the hopes the margins on the internals are small enough to make the share go between 40/60 and 60/40, but for long term or unmonitored use: No! Too many risks.

See @IgnacioVazques-Abrams' comment about insulation materials used to mount TO220 packages with sufficient insulation.

Apart from that, the same risks apply to the LEDs, unless you add balancing resistors there as well. Supposedly this is okay, as you are using linear current control, so 'wasting' another half volt in an extra resistor won't be hurting too much.

To give the full explanation, let's assume one LM317 has a 1.215 reference and the other has a 1.225 reference. If you then add them together at the adjust and output points one device wants to put Vadj+1.225 on the top of the resistor, the other Vadj+1.215. This starts out with them competing a little and then slowly the balance most likely goes more and more to the higher voltage one, heating it more than the other, then the balance can get further out of whack, until the high valued one would have to insert 2.5A into the whole of it, which it will not for long, if at all.