Flow adds to spring a suggestion of abundance or ease of inception.

// words flowed easily from her pen

Some common synonyms of derive are arise, emanate, flow, issue, originate, proceed, rise, spring, and stem. While all these words mean "to come up or out of something into existence," derive implies a prior existence in another form.

// the holiday derives from an ancient Roman feast

While in some cases nearly identical to derive, issue suggests emerging from confinement through an outlet.

// blood issued from the cut