Your question is not clear. But here is a starting for you.

Just adopting Chris answer to same sort of question,

Eq1 = x'[t] == x[t]^2 + 2*y[t];
Eq2 = y'[t] == 3*x[t];
splot = StreamPlot[{x^2 + 2*y, 3*x}, {x, -6, 6}, {y, -6, 6}, 
  StreamColorFunction -> "Rainbow"]
Manipulate[
 Show[splot, 
  ParametricPlot[
   Evaluate[
    First[{x[t], y[t]} /. 
      NDSolve[{Eq1, Eq2, Thread[{x[0], y[0]} == point]}, {x, y}, {t, 
        0, T}]]], {t, 0, T}, PlotStyle -> Red]], {{T, 1}, 0.1, 
  1}, {{point, {0.01, 0.0}}, Locator}, SaveDefinitions -> True]

Your question is not clear. But here is a starting for you.

Just adopting Chris answer to same sort of question,

Eq1 = x'[t] == x[t]^2 + 2*y[t];
Eq2 = y'[t] == 3*x[t];
splot = StreamPlot[{x^2 + 2*y, 3*x}, {x, -6, 6}, {y, -6, 6}, 
  StreamColorFunction -> "Rainbow"]
Manipulate[
 Show[splot, 
  ParametricPlot[
   Evaluate[
    First[{x[t], y[t]} /. 
      NDSolve[{Eq1, Eq2, Thread[{x[0], y[0]} == point]}, {x, y}, {t, 
        0, T}]]], {t, 0, T}, PlotStyle -> Red]], {{T, 1}, 0.1, 
  1}, {{point, {0.01, 0.0}}, Locator}, SaveDefinitions -> True]