Can a Dr refuse to tell a patient about the progress of their cancer after the patient has refused treatment (Chemo)?

Absolutely.   If you refuse treatment,  it's entirely up to the doctor's prerogative. 

The oncologist recommended a treatment plan.
Your father refused.
The oncologist provided no further treatment, effectively your father removed himself as a patient.
Your father would have to get referred  by his regular doctor for further testing.
The oncologist is fully involved with patients who are following treatment plans.

Most are happy to explain various parts of a treatment plan, discuss modifications of a treatment plan etc. 
Sounds like your father opted for no treatment plan at all.

A doctor is not required to treat a patient.
If the doctor would rather spend their time on patients that who are "following doctors orders" or at least using the doctor as a partner in their treatment, that's the doctor's option.

Seems like your dad should select another doctor.  One that he might like to use as a partner in this treatment. 

To vague a question. Would really need context

I read some of the answers and this is a dilemma. I'm not sure why your father went back to the same oncologist. Did the oncologist previously give the impression that your father could go back any time and still be treated? Because that's what it sounds like to me. I don't think the oncologist should refuse to do tests. That seems unethical. And every patient has the right to refuse treatment. Otherwise, oncologists would be forcing differing treatments on people who didn't want a certain treatment. I think your father can get some tests done elsewhere. Or perhaps get the family doctor to refer him to another oncologist at another hospital altogether.