Isolating KI3 from solution
Well, @NilayGhosh already commented on stability of $\ce{KI3}$ in aqueous solution, also $\ce{K+}$ is not bulky enough. But as long as OP didn't mention explicitly that it must be water we isolate potassium triiodide from, there is a workaround, if one desperately want to get its crystals (in an altered form though). 

From isopropanol one relatively easy obtains red diamond-shaped crystals of (18-Crown-6)-potassium tri-iodide (1) as the result of reaction between potassium isopropylxanthate and iodine:



There are also many other examples in the literature showing how one can man make potassium "bulkier", but I found this particular example the most straightforward.

Of course, there is always a fallback option to crystallize ammonium triiodide $\ce{NH4I3}$ (2) as ammonium is probably the closest cation resembling potassium for this case. 

(1) Sievert, M.; Krenzel, V.; Bock, H. Zeitschrift für Kristallographie - Crystalline Materials 2010, 211 (11), 794–797. DOI: 10.1524/zkri.1996.211.11.794
(2) Cheesman, G. H.; Finney, A. J. T. Acta Cryst B, 1970, 26 (7), 904–906. DOI: 10.1107/S0567740870003357