Accent: the way someone pronounces the sounds or words of a language. A person's accent shows which country or which part of a country they come from. You may speak standard British English with an Arabic accent. Someone might have a Scottish accent: his r's will be thrilled. An American might speak Arabic with an English accent. He might say "امل" instead of "عمل".
Dialect is a form of a language which is spoken only in one area, with WORDS or GRAMMAR ( or pronunciation) that are slightly different from other forms of the same language.
In other words, we can say if you have a specific accent, when you write your sentence, it would be the same as mine (with a different accent), but if you speak another dialect, your sentence will be different form mine in writing too. Egyptian is a dialect of Arabic ( some people say it's actually a totally different language, not even a dialect). But if I learn Egyptian Arabic, and pronounce the words like in Persian (فارسی), then people would say, "You have a Persian accent. Are you from Iran?"
Let me know if you need more clarification.