"My cell phone does not have any memory."
Translation:Το κινητό μου δεν έχει μνήμη.
I believe that "κανένας καμία κανένα" are only used with countable nouns (e.g. κανένας άνθρωπος, καμία αμφιβολία) whereas "μνήμη" is a mass noun (something which cannot be counted and has no plural form). "Καθόλου" is the word used to show that there is an absence of a mass noun, so it would be "καθόλου μνήμη".
Other examples with "καθόλου": Δεν έχει καθόλου νερό = There isn't any water Δεν βλέπω καθόλου κόσμο" = Ι don't see any people (in English we would use the plural here)
Well, it may be that if you are a mobile phone technician this would be the case, so on a technicality it might be regarded as correct. But for 99.99% of the populations to say a mobile phone has "memories" would be considered wrong. And I suspect that Yannis49's excellent explanation above would apply to 99.99% of Greeks.