you could spray the TLC plate with dithizone which forms a purple (red) complex with zinc(II). A disadvatange could be the intrinsic color of dithizone (green).
you could perform thin-layer chromatography on silica gel 60 plates with eluent methanol/water 50:50 or 70:30 (v/v) and stain the plates after drying with a dilute solution of dithizone in acetone and then dry again with a heat gun. Maybe it could work, but TLC of anorganic salts is generally difficult. Zinc sulphate would have a low Rf value and probably tend to smear on the TLC plate. Moreover, other metal cations than Zn(II) interfere with dithizone, since dithizone (diphenylthiocarbazone) builds colored complexes with many metal cations [Ag(I), Bi(III), Cd(II), Co(III), Cu(II), Hg(II), Pb(II), Tl(I) etc.].