A good machine learning approach for distribution of a whole? So I had done with different classification, regression and clustering approaches for predictions of values etc. I was wondering if there is a machine learning approach for distribution of a whole based on on some features (I do not know if there is an approach for that I just could not find one with my research). 

An easy example might be lets consider we have height and weight data of many children and we have to distribute a given number of pizza slices amongst them so that skinny children gets more pizza as compared to obese ones because pizza is more beneficial for skinny as compared to obese. So might have to find out the optimum number of slices for each child out of the total number of slices so that each child gets maximum possible nutrients. A more complex version could incorporate more features like age, overall health, blood sugar content, physical activity index, daily calorie consumption and others.

A similar example might be to find out the optimal value of fuel to be allocated to each vehicle if we have a total of 100 gallons. Features might be distance they have to travel, mpg, driver competency, engine horse power etc so that all of them might travel the maximum distance possible.

So can we achieve a task like this with machine learning/deep learning approaches? If not what are the hurdles achieving this?
The example you describe looks more like an optimization problem, possibly related to operations research but I'm not sure.

Naturally ML can be used to approximate the optimal solution(s) for this kind of problem. For example genetic algorithms are a common way to find the "approximately best" solution to an optimization problem.

This kind of problem can also sometimes be formalized as a regression problem, depending on the exact constraints to satisfy.