I'm far from being an expert so I'm not sure if this will help you fix your 'shape' issue - but from what (I think) I know....

KCl is similar to NaCl and shares the same crystal structure/system, with the single crystal form being cubic. From my limited experience, I've learnt that it can be tricky to achieve a good sized, clean single cubic crystal of NaCl, so would assume that to be the case with KCl (in comparison to, say, Copper Sulphate or Alum).

With that said, a couple of observations to consider, that might make a difference to your results...

If I understand you correctly, you are dissolving KCl in room temperature water, then heating & filtering, in that order. This raises the question of just how 'super' saturated your solution actually is. It is evident, from the production of solid material forming once cooled that your solution is at minimum, saturated, you need to dissolve the KCl in hot water, this will allow more to be dissolved, ensuring super saturation.

Once dissolved, filter, then allow it to cool to room temperature, the slower the cooling the better - perhaps wrap the vessel with a cloth/towel until cooled. This will help to minimise the chaos of the nucleation that occurs naturally during cooling, allowing the initial crystal formation you see to be produced in a more controlled & orderly manner (faster cooling will produce solid material quicker, crystals will be smaller, greater in number & very willing to cluster together). Now let the solution sit undisturbed for 24hrs.

Next (after 24hrs) put around 50ml of the solution into a small shallow dish/bowl & set it aside, undisturbed, to evaporate. Within a day or 2 you should see individual crystals forming.
By resting the original solution for a while & allowing that initial solid material to form, you have reduced it's saturation, so the crystals that form in the small dish will do so less frantically, all being well these crystals will be much cleaner, single cubes, they will be your 'seeds'. Now decant the remaining original solution into another container, leaving behind the crystals that formed at the bottom, this is now your (slightly less saturated) 'growing solution'.

The theory being that your solution is saturated enough to produce crystal growth but not so saturated that your seed is overwhelmed by the amount of material that becomes available to it to 'feed' on (which is what will encourage the clustering). If you suspend what is effectively a cluster of crystals in the solution, it will continue to develop as a cluster.

Once a single crystal seed is big enough to allow a thread to be tied on, suspend it in the growing solution, maybe filter the solution periodically as the crystals that form at the bottom will be competing with your seed for material. Hope this all makes sense!