It depends on the type of flux. Most no-clean rosin flux (common in standard rosin-core solder) can be left in place for prototype use; it is non-conductive and non-corrosive once fully cooled. For a finished product or any circuit operating in a humid environment, cleaning is a good habit regardless.

Water-soluble flux must be cleaned off after soldering. If left on the board, it absorbs moisture and can cause corrosion and leakage currents.

To clean flux residue, use isopropyl alcohol (IPA) 90% or higher and a stiff brush (an old toothbrush works well). For stubborn residue, a dedicated flux remover/PCB cleaner is available from electronics suppliers. Always let the board dry fully before powering it up.