Shouldn't "ridiculously (adverb)" be used here to be grammatically correct? Because I've seen few cases using "adverbs" after the verb "sound."
If he were describing the way in which he speaks, then you would be correct, and he should have said "ridiculously" since this is an adverb and "speak" is a verb. However, he is not describing the way in which he speaks in this context. Instead, he is joking that he doesn't "speak ridiculous", as though "ridiculous" were its own language. Thus, "ridiculous" in this case is used as a noun.