Solder wire intended for electronics normally has the required flux in the wire, it's just that SnPbCu and SnPbAg flux is a bit more agressive. There are SnAg solder wires that require >300 deg C and a separate flux (don't know what the composition is, when I used this, the flux bottle came bundled with the solder wire and actually cost almost as much as the expensive wire!).
There are flux sprays as well as eyedropper and brush-on liquids, which can be of great help for SMD components and NOS silvered or silver wire components when the silver has tarnished. In any case, I would take any flux residue off the board. Flux is normally heat activated, but that only means it's chemically agressive action is slowed down a lot at room temperature - in essence, it WILL eventually degrade the board and/or attract moisture and partciles, it will just take a long time. Still, it's really not a big investment to clean it off and you get a pristine board which will never have problems of that kind.