Hi Autismmom
Its a big subject, and I'm not a reflexologist .... but my son did have speech problems when he was younger, (and other problems... but we didn't go down the conventional diagnosis route ...) Anyway in his case fluoride was his main problem and once intake of that was stopped, his usual not wanting to move much changed and he was constantly bouncing up and down on a mini trampoline for a while ... trampolining apparently stimulates the speech centres .... so depending on any sensory issues, the gentle stimulation of the feet by reflexology might be useful.
From general speech problems at 4 my son went onto only have speech problems when he was stressed, to being able to read and speak separately but having problems reading aloud, to no longer having speech problems.
His speech problems were less severe, (and he was food phobic rather than having a swallowing problem) and I don't think we would have reached the point we did if we hadn't found out about how fluoride was affecting him. (I'm not saying fluoride is the root of all evil ... but some people are less able to handle it, and it was a big factor for him personally).
So on a direct level, I think that reflexology may be worth trying, and also on a "stress management" level, but you will probably need to find a therapist who is knowledgable about autism for any sensory issues etc etc and who would be able to suggest alternatives if working with the feet wasn't an option.
Certainly in my son's case he went from hating his feet touched (and nail cutting was traumatic) to after fluoride intake was stopped to liking having his feet massaged. He wouldn't (at the most challenging times) have let anyone touch his head (for IHM example). Hair washing was a nightmare for him.
I think he'd choose foot massage to head massage even now, but for some people head massage is great, but having their feet touched isn't ....
Hope that helps.