How to generate synthetic dataset using machine learning model learnt with original dataset?

The general approach is to do traditional statistical analysis on your data set to define a multidimensional random process that will generate data with the same statistical characteristics. The virtue of this approach is that your synthetic data is independent of your ML model, but statistically "close" to your data. (see below for discussion of your alternative)

In essence, you are estimating the multivariate probability distribution associated with the process. Once you have estimated the distribution, you can generate synthetic data through the Monte Carlo method or similar repeated sampling methods. If your data resembles some parametric distribution (e.g. lognormal) then this approach is straightforward and reliable. The tricky part is to estimate the dependence between variables. See: https://www.encyclopediaofmath.org/index.php/Multi-dimensional_statistical_analysis.

If your data is irregular, then non-parametric methods are easier and probably more robust. Multivariate kernal density estimation is a method that is accessible and appealing to people with ML background. For a general introduction and links to specific methods, see: https://en.wikipedia.org/wiki/Nonparametric_statistics .

To validate that this process worked for you, you go through the machine learning process again with the synthesized data, and you should end up with a model that is fairly close to your original. Likewise, if you put the synthesized data into your ML model, you should get outputs that have similar distribution as your original outputs.

In contrast, you are proposing this:

[original data --> build machine learning model --> use ml model to generate synthetic data....!!!]

This accomplishes something different that the method I just described. This would solve the inverse problem: "what inputs could generate any given set of model outputs". Unless your ML model is over-fitted to your original data, this synthesized data will not look like your original data in every respect, or even most.

Consider a linear regression model. The same linear regression model can have identical fit to data that have very different characteristics. A famous demonstration of this is through Anscombe's quartet.

Thought I don't have references, I believe this problem can also arise in logistic regression, generalized linear models, SVM, and K-means clustering.

There are some ML model types (e.g. decision tree) where it's possible to inverse them to generate synthetic data, though it takes some work. See: Generating Synthetic Data to Match Data Mining Patterns.