captaan - no.
You have it the wrong way round. Induced drag is greater at low speeds, form drag greater at high speeds. Really I need to draw a graph to illustrate how it works, but that is probably beyond my PPrune posting skills.
Form drag, for a given body and attitude and atmospheric condition, and ignoring compressibility, is proportional to speed squared.
Induced drag is inversely proportional to speed squared. You can show mathematically that an aircraft's min drag speed is the speed at which induced drag and form drag are equal. You can fly more slowly - that's when you are "on the wrong side of the drag curve" and speed is unstable - you need a whole armful of thrust to recover from a speed reduction.
For a given span, induced drag is minimum if the spanwise distribution of lift is elliptical - again that can be shown mathematically. You can achieve that with an elliptical wing (e.g Spitfire) or by more subtle means of changing thickness and wing section.
Yes, flap extension will change the spanwise lift distribution, as remarked by previous contributors, and since the wing (on a transport aircraft) will be optimised for cruise, you can say with some certainty that induced drag will then increase.