  A triangle-path in a graph $G$ is a sequence of distinct triangles
$T_1,T_2,\ldots,T_m$ in $G$ such that for any $i, j$ with $1\leq i < j \leq m$,
$|E(T_i)\cap E(T_{i+1})|=1$ and $E(T_i)\cap E(T_j)=\emptyset$ if $j > i+1$. A
connected graph $G$ is triangularly connected if for any two nonparallel edges
$e$ and $e'$ there is a triangle-path $T_1T_2\cdots T_m$ such that $e\in
E(T_1)$ and $e'\in E(T_m)$. For ordinary graphs, Fan {\it et al.}~(J. Combin.
Theory Ser. B 98 (2008) 1325-1336) characterize all triangularly connected
graphs that admit nowhere-zero $3$-flows or $4$-flows. Corollaries of this
result include integer flow of some families of ordinary graphs, such as,
locally connected graphs due to Lai (J. Graph Theory 42 (2003) 211-219) and
some types of products of graphs due to Imrich et al.(J. Graph Theory 64 (2010)
267-276). In this paper, Fan's result for triangularly connected graphs is
further extended to signed graphs. We proved that every flow-admissible
triangularly connected signed graph admits a nowhere-zero $4$-flow if and only
if it is not the wheel $W_5$ associated with a specific signature. Moreover,
this result is sharp since there are infinitely many unbalanced triangularly
connected signed graphs admitting a nowhere-zero $4$-flow but not $3$-flow.
