He can apply, but the income he is receiving from his Disabled Adult Child benefits may put him over the resource limits for SSI. Basically, SSI is a need-based program that considers income that a beneficiary receives in determining eligibility. SSI has a maximum benefit rate of $721 per month. If your son is currently receiving SSDI benefits over $721 a month, then he will be over the resource limits for SSI and not eligible for SSI benefits. If his SSDI check is under this amount, then it might be worth applying.
If he is eligible for some SSI benefits, understand that you can't double dip with SSI. SSI is meant to be a supplement. For instance, if he is getting $500.00 a month in Disabled Adult Child Benefits, then he might be eligible for a $241 check. (The combined maximum rate for those receiving both SSI and SSDI checks is $741).