Influence of solubility on the complexation constants at different pH values
It is possible to calculate out all of the complexation and speciation reactions using the concepts of Aquatic Chemistry. I’m a PhD student in environmental chemistry and I TA a course in Aquatic Chemistry. Usually, when pH matters it’s because the protonation state controls the chemistry and can be described using equilibrium constants. I bet that your solubility issue is related to the deprotonated form being an anion and thus more soluble in water than the protonated, neutral form (very common for organic compounds). The protonation state can be calculated from the $\mathrm{p}K_\text{a}$:

$$
\ce{L- + H+ &lt;=&gt; HL}\\
K_\text{a}=10^{-\mathrm{p}K_\text{a}}=\dfrac{[\ce{L-}][\ce{H+}]}{[\ce{HL}]}
$$

Where $K_\text{a}$ is the equilibrium constant, and L is your compound. I would guess that your flavanoids and cyclodextrins might have multiple $\mathrm{p}K_\text{a}$s, you can write an expression like this for each one.

Complexation reactions can be written in a similar way. Let’s say that $\ce{Y}$ is the molecule your $\ce{L}$ molecule complexes with, and it is neutral when protonated ($\ce{HY}$).

$$
\ce{L- + HY &lt;=&gt; HLY-}\\
K=\dfrac{[\ce{L-}][\ce{HY}]}{[\ce{HLY-}]}
$$

Where $K$ is the equilibrium constant for this complexation reaction. Keep in mind that which species (protonation state) is in the expression matters, the value for the equilibrium constant is only valid for those species. Above, I’ve written that the deprotonated form of L ($\ce{L-}$) complexes with the protonated form of Y ($\ce{HY}$). This is where pH comes in. pH controls how much of L is deprotonated and how much of Y is deprotonated and able to participate in complexation, and $K$ controls how much of the available $\ce{L-}$ and $\ce{HY}$ form the complex. Complexes themselves can also have $\mathrm{p}K_\text{a}$s the one above ($\ce{HLY-}$) could probably be protonated to a neutral form $\ce{H2LY}$.

You might be able to guess that the mathematics gets a little complex at this point. It is possible to do these calculations by hand, but there are computer programs that can handle them. The most easily accessible one is Visual MinTEQ. The other hard part is having the data for the equilibrium constants, there may be data for your system, but you’ll have to look.

Just to summarize. Complexation constants don’t change with pH (they are, in fact, constant) it’s just that the speciation matters, and speciation is controlled by pH. The ‘global constant’ you refer to is pH, not something else.