I use flowcharts all the time to map out orders of operations.
If you mean "order of operations" in the sense of "overall data flow of a program", then flowcharts are an absolute must. There come to be certain diagrams that everybody has a copy of, and that are seen on whiteboards all around the office because they are so important/common. eg, a diagram to describe that "Data from the application, is encapsulated using a UDP header, and then travels to the IP layer, where a header is then added..."
If you mean "order of operations" in the "how does this code work" sense, then yes - flowcharts absolutely help there as well. "The first thing we do in this routine is compute the checksum. Then we pass the pointer to the next routine and set a timer. The callback function for the timer is..."
If you mean "order of operations" as the mathematical evaluation of expressions, then this can be important as well when trying to understand someone's code, or when trying to write your own algorithm. "First we increment the pointer, and then we dereference it so that we can read the value..." or "We need to right-shift the integer 32 times, check for the presence of a 1, and then..." These are sometimes algorithm flowcharts, or sometimes operator flowcharts. In either case, they are useful to understanding what is going on without having to mentally parse code.
That is to say, they are not a crutch at all.
Some things to note: with the mathematical evaluation... often, if an expression is not easily readable (many nested operations or parentheses, may operators of many different precedence - like dereferencing, incrementing, and arithmetic), it might be better to break the code into multiple smaller steps. That way you can easily show the logic of the calculation, as well as the implementation. You might still need a flowchart, but the code itself reads easier.
Finally, more advanced/experienced programmers sometimes don't need as many flowcharts. They already have the relevant diagrams memorized, or they can parse logic better because they recognize certain idioms. You will certainly develop that, if you haven't already. But in the meantime, there is no reason not to use flowcharts if you need to understand something. Not a crutch at all!