My guess is this is the kind of algebra you **don't** care about (since they contain no geometric information), but algebras of the form $\mathbb{R}[x]/x^n$ will have your property.  When looking for a flow corresponding to a derivation $\xi$, consider the formal power series
$$ \sum_i \frac{t^i\xi^i}{i!} $$
The problem, of course, is showing that this power series converges in the algebra of appropriate endomorphisms.  However, a lazy trick for guaranteeing its convergence is to hope that $\xi^n=0$ for some $n$.  This happens for every derivation in the ring $\mathbb{R}[x]/x^n$, or more generally when the nilradical is maximal.