How to integrate transcriptomics data with kinetic metabolic models?
I am assuming that in your model, the reactants and products (species) are metabolites and each reaction denotes conversion of one metabolite to another. 

From transcriptomics, you will get the relative expression levels of different genes. 
When you have two samples from different conditions you can calculate the differential expression. 

A model can be as complex as you can make it but we can start with simple assumptions. As you said, enzymes are assumed to be constant with respect to metabolites and are not dynamically changing. I also guess that you are not considering genes other than enzymes to be affecting the metabolic reactions (you might actually want to consider the solute transporters). Also, you are assuming Michaelis-Menten kinetics for all reactions. 

In that case your Vmax (i.e. maximum rate of a reaction) would be kcat × E0 where kcat is the turnover number and E0 is the total amount of enzyme. 

E0 can be approximated using the transcriptomics data. However, transcriptomics data is relative and not absolute. If you need absolute quantification, you must have at least one reference whose absolute mRNA copy number is known. Another issue is that the ratio of protein and mRNA expression would not be the same for all genes and it is basically the amount of active protein you need to know. So proteomics would be one step closer.

When you are comparing two conditions, you can use the differential expression (fold change values) to adjust the parameters between the two conditions. For e.g. if you know that phosphofructokinase is 2 fold downregulated in diabetes (compared to healthy case) then you can reduce the Vmax of the corresponding reaction by 2 fold in your diabetes model. However, it all would make sense only if the parameters of your "healthy" model are reasonably close to the biological reality.

Moreover, you still need to know kcat. It cannot be obtained from high throughput studies. You may have to either make some guesses or check out papers/databases. Also, your rate is not always Vmax. To estimate the dynamic rate you must know KM too (when the substrate is in excess you can ignore KM). BRENDA may have some information about these constants for different enzymes.  

At a very crude level, you can remove the reactions whose corresponding enzymes have zero expression. 



These are some articles on integration of transcriptomics data with FBA (not kinetic models):


Blazier and Papin (2012)
Machado and Herrgård (2014) 
Guo and Feng (2016)


Machado and Herrgård actually claim that integration of transcriptomics data does not improve their model predictions:


  Also, it is observed that for many conditions, the predictions
  obtained by simple flux balance analysis using growth maximization and
  parsimony criteria are as good or better than those obtained using
  methods that incorporate transcriptomic data.