I started with Jack's classic and Jack's all purpose during the first 3 weeks of flowering and then switched to Fox Farm tiger bloom and big bloom. It's been 4 weeks since I switched to organic nutes, do my plants still require flushing?
Flushing is only necessary in the event something is wrong with the medium. Generally flushing can be useful in the event of over fertilization as one wants to remove any excess fertilizer from the medium to avoid further damage to the plant.
Flushing doesn't affect the end product and really can end up causing more problems if you have a deficiency and believe it to be over fertilization. One can end up water damaging the roots in such an instance.
Just ramp down fertilizing at the end, and use water for the last couple weeks as the plant requires less nutrients and will use up what's left in the medium.
Eta fox farms states it's organic, and it is to a degree. I did the opposite of you and went from fox farms to jacks. I could never imagine going back to fox farms as it was very salty and lacking N in bloom. I had more problems with FF than I've ever had with Jacks. Only issue I ran into with Jack's is calcium deficiency with longer flowering plants. Easily solved by amending Happy Frog with Dolomite lime prior to using my mix of 60/40 Happy Frog/Perlite.