An Etymological Dictionary of the German Language/Fleiß
Fleiß, m., ‘industry, application, diligence,’ from MidHG. vlîȥ, OHG. flîȥ, m. ‘diligence, zeal, care,’ OHG. also ‘contest,’ from OHG. flîȥȥan, MidHG. vlîȥen, ‘to be zealous, apply oneself, ModHG. befleißen, partic. be-, geflissen. Comp. Du. vlijt, ‘diligence,’ AS. flitan, ‘to emulate, quarrel, contend,’ E. to flite. On the evolution of meaning see Krieg. ‘To emulate’ seems to have been the lit. meaning of the merely West Teut. root flī̆t (Goth. fl- or þl-? — see fliehen). No further references have been discovered.