Both could be ok depending on context. "Speak aloud" would be in contrast to just thinking the words. "Speak loudly" would be in contrast to speaking quietly. This advice would be likely given before the person had begun speaking. You could also say "Speak louder" if the person was already speaking, but too quietly.

Dictionary definitions are loud = speak with high volume. Shout Aloud = speak clearly with clear diction so that your voice carries across the open space of a Theatre/theater or meeting room with no microphone or amplifier. like an actor. Good actors are either natural clear orators or they are trained to be clear speaking aloud voice throwers.