There is no female doctor in her town; can she give birth with her maternal uncle who is a doctor?

Praise be to Allah.

The basic principle is that women should be treated by women, as has been explained in the answer to question no. 5693 and 120224. 

It is permissible to be treated by a male doctor if there is no female doctor, whether she is Muslim or kaafir, or when there is a need for particular skills or specialization which cannot be found with a female doctor. 

If the matter is as you describe, and there is no female doctor in your town, and going to another town will cause you health and physical problems, then there is nothing wrong with your going to a male doctor, whether he is your maternal uncle or someone else.  But he should appoint some nurses to directly supervise your birth and guard you from the view of the male doctor, except in a case of urgent need. 

And Allaah knows best.