It originated from "guns all blazing", but it's idiomatic meaning is a little different.
When you say 'guns a-blazing' you are injecting a little humour (rightly or wrongly) or sarcasm into a situation where guns are being fired almost comicly in a repeated,noisy, and somewhat haphazard (not accurate) fashion - Similar to a western movie where a gunslinger comes out and fires repeatedly and noisily at someone in the street.
If you said 'guns all blazing' there is no obvious injection of humor. So while 'guns a-blazing' has it's origins in 'guns all blazing' the expressions say different things.