Bounding Rademacher Averages, with and without chaining One can bound the Rademacher average $R_n(A)$ of a finite set of vectors $A\subseteq\{0,1\}^n$ using Massart's Finite Lemma:
$$
R_n(A)\le \max_{a\in A}\|a\|\frac{\sqrt{2\ln|A|}}{n}
$$
where $\|\cdot\|$ is the Euclidean norm.

Then, using Sauer's Lemma, one can obtain 
$$
R_n(A)\le C\max_{a\in A}\|a\|\sqrt{\frac{V\ln\frac{n}{V}}{n}},$$
where $V$ is the (empirical) VC-dimension.

Using chaining and a bound on covering numbers, one can get rid of the logarithmic factor and obtain
$$
R_n(A)\le C'\sqrt{\frac{V}{n}}.
$$

Looking at the proof that uses chaining, I can't seem to find a way to have $\max_{a\in A}\|a\|$ in the second bound. Is it even possible?

It may not change much in theory, but it does in practice, and (in my opinion), it intuitively makes sense that the bound should depend on it.
Converting the comment to an answer: See the notes here: 
cs.cornell.edu/~sridharan/dudley.pdf
with the dependence on $\sup_f \hat E[f^2]$