Is this sentence correct?
I am starting learning xyz.
It is, but I am starting to learn xyz might be preferable, if only to avoid the sound of the two -ing forms one after the other.
This statement is not wrong in popular English -- but in "formal" contexts you should prefer something like:
I am starting to learn xyz.
But, sometimes the former is more suitable. For example
I'm practicing dancing.
is more common (even formally), than
I am practicing to dance.
Hence, the bottom line is: use what people are accustomed to hear and read. (unless of course it's a new coinage)