Suppose StreamPlot starts by calculating what to display for x= -2 and y= -2.

So it calls myGradient[-2,-2]

Your definition of myGradient then starts to calculate Grad[myFunction[-2,-2],{-2,-2}]

You can probably see how that is going to be a problem.

You might try removing the : and thus changing your code to

myGradient[x_, y_] = Grad[myFunction[x, y], {x, y}]

That graph will display, but might look a little odd, changing your function to x^2 - y^4 might give a StreamPlot that looks more reasonable.

What the differences are between := and = and exactly why the evaluation does what it does in your example is a deeper issue. Understanding the depths of how evaluation works in Mathematica is key.

You also need to be aware of any cached prior definitions of functions which can sometimes change the behavior that you might be expecting. Those might be responsible for some of the problems you are seeing. You can quit the kernel or clear individual definitions or restart Mathematica to eliminate those.

try this: EquationTrekker

EquationTrekker is one way to plot differential equations in Mathematica and not the easiest to find in Help (it's mentioned somewhere).

EquationTrekker has an interface for plotting (gradients) in the way it plots them.

https://reference.wolfram.com/language/EquationTrekker/tutorial/EquationTrekker.html