Relative vertex capacity in max flow algorithm
For edge "consumptions" I believe the following approach should work: [I misread your question at first, but am leaving this part for the benefit of future people reading this]

Suppose you have some edge $u\rightarrow v$ with "consumption" $c$. Then you can model this by inserting a vertex $w$ in the middle to get $u\rightarrow w \rightarrow v$ and then add an edge $w\rightarrow t$ with capacity $c$, where $t$ is your sink. Then you have to ensure that your max-flow algorithm prioritizes pushing flow through $w\rightarrow t$ over $w\rightarrow v$. Thus this flow will be "consumed" as much as possible before going through the edge. I see two ways in which this can be done:


If your algorithm works by finding an augmenting path, make sure that this augmenting path goes through $w\rightarrow t$ rather than $w\rightarrow v$ if possible (i.e. if $w\rightarrow t$ is not saturated). Also make sure that this holds for the "reverse edges" (i.e prioritize taking flow away from $w\rightarrow v$ rather than $w\rightarrow t$). This should not be difficult to do, but depends on the exact implementation, and on your access to it.
Or you can use a max-flow min-cost algorithm and give a positive cost (say 1) to every edge except those of the $w\rightarrow t$ type (who receive a cost of 0).


Then to get the answer to your original problem just ignore all the $w\rightarrow t$ edges.

Now, for vertex $v$ with "consumptions" $c$ you can simply add an edge $v\rightarrow t$ with capacity $c$ and modify your algorithm in the same way.

If you don't care about the exact value of the flow through each edge but only the total max-flow, then you don't even need to change anything to the algorithm and can just use the returned value for the new graph as is.