Excellent question. I have not really thought of this before. To really break down the differences you have to go back to the definition of "form" and "kind". In looking at the English definition of "Form" you will notice that it has to do with the shaping and creation of an object. So typically when you utilize the phrase "form of..." you are comparing an object to something similar but slightly different. Example: "The alien took the form of a man." This can be used for non-physical things too. "He inserted a compliment in the form of a criticism." In this case, the subject is forming/shaping a compliment as if it were a criticism. "Kind of" is more of a phrase for categorizing things. The definition google provides is literally "A group of people or things having similar characteristics." So while characteristics may include form and shape, the phrase "Kind of..." implies that you are categorizing something.

a form of ... a mode, type or essence of something. Examples: A form of flattery, (a type of flattery) a form of affection, (like a kiss for example, an action that shoes affection.) a kind of, something similar or nearly like something else. Examples: a kind of athlete (like an athlete but maybe not the typical kind) a kind of vehicle, (a ATV for example) a kind of apple ( say a fuji apple, the type of apple)