Measuring ADC sample rate - Arduino DUE
I think using an interrupt controlled measurement might provide the best results for you.

Note: you might get more complete feedback using the Arduino forum.

In general the process would look like this:


Set up an interrupt vector for the ADC peripheral (in this case support for ID37).
Setup ADC registers (res, clock etc)   
Set up a timer to time the conversion.
Create Active flag and Timer variables for processing inbound timer values.
Start timer and ADC conversion.
Loop waiting for active flag to set (it gets set in the ISR), when detected do average or store timer values, then clear active flag.


This methodology times each individual conversion using a high speed timer, which could mean a lot of values to process. You could equally not time each conversion, but simply set up say a 1 second timer, and count the total number of conversions in 1 second for your particular ADC configuration. 

Peripheral ISR


Waiting for Interrupt.
In peripheral ISR, read and store timer value, reset timer, set active flag 
Return from ISR