The OED has 7 noun entries for chat but most of them are obscure, regional, or obsolete. No mention is made of full chat or flat chat, which I suppose, for want of any better idea, to be related to chat = “talk”, though I don’t see how. (Edit: I’ve never heard either expression in the US.)
In the US, we have the “talk” sense of chat, both noun and verb, and less familiarly it’s also used as a term for a kind of crushed rock, coarser than gravel, and in the names of a some species of birds ("yellow-breasted chat”, etc.).
In the sense of “at maximum speed, rate, or extent” we have full tilt and flat out. Are these used in the UK and Australia?