Summary: Try one of the extensions of FBA which take gene regulation into account, but be aware of the limitations. See below for references.
There are two approaches to estimating internal metabolic fluxes: The (primarily) experimental and the (primarily) computational. I say primarily, because even for the experimental approach, a large amount of computation need to be done, and for the computational approach, experimental studies must be consulted in order to set realistic model parameters.
Experimental determination of internal metabolic fluxes has been centered around 13C-metabolic flux analysis (13C-MFA) performed through carbon-labelling experiments, as mentioned above. 13C-MFA is complicated and expensive, so there is a relative lack of experimental data, and most experiments cover only a few fluxes when compared to the number of possible reactions, typically several thousand in genome-scale metabolic models. In 13C-MFA, most experiments estimate the fluxes in a much smaller model (for example the central carbon metabolism), avoiding or ignoring other possible reactions, and the set of fluxes that are estimated varies between experiments.
Models which are used in computational approaches to flux analysis are typically larger than the models used in 13C-MFA experiments, and thus it is usually not possible to determine all the fluxes from experimental data alone. Thus, an approach called constraint-based modelling (COBRA) is mainly used. The basic assumption of most current flux analysis methods, both experimental and computational, is that metabolite concentrations are at steady state. Mathematically, this can be described by the equation
$S\overrightarrow v = 0$
where $S$ is a stoichiometric matrix relating the metabolites and all possible reactions (basically a compact description of the metabolic model), and $\overrightarrow v$ is the flux vector containing all the flux values. In addition to the steady state requirement, constraints are typically applied to the uptake and excretion rates of various metabolites, limiting them to biologically realistic values. Other requirements, such as requirements for ATP maintenance consumption can also be applied.
Because there are typically many possible flux patterns that obey the above constraints, a principle is needed for selecting a biologically realistic solution from the solution space of feasible flux patterns. Assuming that cells optimize their metabolic patterns in some way, different objective functions are used that attempt to capture the metabolic behaviour for cells. Once an objective function is chosen, the set of possible solutions can be searched for the flux pattern that gives the highest objective value as a function of the flux vector. Given that the objective is linear (simply a weighed sum of fluxes), an optimal solution can be found rapidly. In general, many different optimal solutions may exist for a given objective function. The method of applying an objective function to a constrained metabolic model at steady state is called Flux Balance Analysis (FBA).
The most basic and a popular objective is maximization of biomass production. While useful for determining maximal growth rates, this objective is unlikely to be realistic when applied to human cells. FBA and related methods is generally well-suited to determining performance limits for single endpoints such as growth rate or production of a single metabolite, but not capable of precisely determining all internal metabolic fluxes. The point that many optimal solutions may exist for a single objective function is important in this regard.
As 13C-MFA and FBA are based on the same concept of metabolite balancing, they can be viewed as different ends of the same spectrum, from purely experimental to purely computational, with 13C-MFA constrained FBA (where 13C-MFA results is used to constrain the possible fluxes in a model before optimizing an objective function, or minimizing the difference between the experimental fluxes and the FBA solution, subject to additional constraints) in the middle.
For an introduction to Flux Balance Analysis, see Orth, Thiele & Palsson: "What is flux balance analysis?" Nature Biotechnology 28 245-48 2010.
For performing Flux Balance Analysis, several software packages are available. One of the most used is the COBRA Toolbox for Matlab. A version for Python called CobraPy is also under development. Both are available at http://opencobra.sourceforge.net/openCOBRA/Welcome.html
Note that most gene-expression data only shows relative changes in expression between two conditions. Most methods are thus based on comparing two different conditions. More recently, RNA-sequencing (RNAseq) may also be used to obtain more direct measures of gene expression levels. Many extensions and variations on FBA have been published which take into account gene expression. Some of these are regulatory FBA (rFBA, Covert & Palsson: Journal of Biological Chemistry, 2002 277, 28058-28064), Metabolic Adjustment by Differential Expression (MADE, Jensen & Papin: Bioinformatics. 2011 Feb 15;27(4):541-7 ) and iMAT (Schlomi et al: Bioinformatics (2010) 26 (24): 3140-3142.). For a more recent method, gx-FBA (gene expression-FBA), see *Navid & Almaas, BMC Systems Biology 2012, 6:150).
You may also want to read this article which deals with construction tissue-specific metabolic models: Computational reconstruction of tissue-specific metabolic models: application to human liver metabolism. Mol Syst Biol. 2010 Sep 7;6:401. doi: 10.1038/msb.2010.56.
The problem with using FBA and related methods to estimate internal fluxes is that validation of the results is difficult because of the mentioned lack of experimental data. I wrote a project report on the topic during the last year of my Master's, which includes a basic description of 13C-MFA. It can be read at http://www.slideshare.net/jarlemag/rapport-31295058