Mostly curious if they tend to pick up their local geographic dialect, or whether there's a specific 'flavor' to ainu-accented speech. I know there's probably < 100 actual Ainu speakers left, but I figure someone might know.
Jesus on the Dashboard
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Dialects/accents are not passed down genetically. The vast majority of remaining Ainu in Japan speak Japanese as their native language, and like you said, the accent they pick up depends on where they grew up. But it's possible that Ainu influenced the Japanese dialects spoken in Hokkaido. I'm not knowledgeable enough in the subject to say.
Rotbuche
Before the Ainu were conquered by the Japanese, they spoke their own language. Nowadays they speak the Japanese language of their region, like the first answerer said.