The authors consider a compact smooth Riemannian manifold \((M,g)\) without boundary, and its Ricci flow, which is a smooth family of metrics \( (g(t))_{t\geq 0}\) satisfying \(\partial _{t}g(t)=-2\mathrm{Ric}(g(t))\), where \(\mathrm{Ric}(g(t))\) denotes the Ricci curvature tensor of \(g(t)\), with the initial condition \(g(0)=g\). This equation is equivalent to \[\partial _{t}g(t)=-2\mathrm{Ric}(g(t))+\mathcal{L}_{W(t)}g(t), \qquad g(0)=g,\] where \(W(t)\) is the de Turck vector field defined in terms of the Christoffel symbols for the metric \(g(t)\) and a background metric \(h\) as \(W(t)^{k}=g(t)^{ij}(\Gamma _{ij}^{k}(g(t))-\Gamma _{ij}^{k}(h))\). The first main result proves that the singular Ricci-de Turck flow preserves the initial regularity of the Ricci curvature. In particular, if the initial metric has bounded Ricci curvature, the flow remains of bounded Ricci curvature. The authors prove that an admissible Riemannian manifold with isolated conical singularities and positive scalar curvature admits a singular Ricci-de Turck flow preserving the singular structure and under the additional assumption of strong tangential stability, preserving the positivity of the scalar curvature along the flow. They recall the definition and properties of conical manifolds, weighted Hölder spaces on conical manifolds, Lichnerowicz Laplacian, and tangential stability. Assuming that \((M,g)\) is a conical manifold, which is tangentially stable and \((\alpha ,k+1,\gamma )\)-Hölder regular, the authors prove the existence of some \(T>0\), such that the Ricci-de Turck flow starting at \(g\) admits a solution \(g(\cdot )\) in the Hölder space defined as \[\mathcal{H}_{\gamma _{0},\gamma _{1}}^{k,\alpha }(M\times \lbrack 0,T],S)=C_{ie}^{k,\alpha }(M\times \lbrack 0,T],S_{0})_{\gamma _{0}}\oplus C_{ie}^{k,\alpha }(M\times \lbrack 0,T],S_{1})_{\gamma _{1}}^{b},\] with \(\gamma _{0},\gamma _{1}\in (0,\gamma )\) sufficiently small, if \((M,g) \) is not an orbifold, and through a slightly different definition if \((M,g)\) is an orbifold. They then write the equations which describe the evolution of the Ricci tensor and of the scalar curvature in the case where \(M\) is a smooth manifold. The second main result proves that if \((M,g)\) is a strongly tangentially stable conical manifold of dimension at least 4, with \((\alpha ,\gamma ,k+1)\)-Hölder regular geometry, with \(\gamma >3\), and \(g(t)\), \( t\in \lbrack 0,T]\), is the solution to the Ricci-de Turck flow with initial metric \(g\) and reference metric either equal to \(g\) or to a conical Ricci flat metric, in which case \(g_{0}\) is supposed to be a sufficiently small perturbation of \(\widetilde{g}\) in \(\mathcal{H}_{\gamma ,\gamma }^{k+2,\alpha }(M,S)\), if \(Rg\geq 0\), then \(R_{g}(t)\geq 0\) for all \(t\in \lbrack 0,T]\). Furthermore, if \(Rg\) is positive at some point in the interior of \(M\), then \(R_{g}(t)\) is positive in the interior of \(M\) for all \( t\in \lbrack 0,T]\). The authors here use properties of the Laplace-Beltrami operator and apply maximum principles.