Ok.
But I think if you want to describe a series of 1st order reactions a -> b -> c you should reformulate your equations.
sol = DSolve[{
D[fa[t], t] == - k1 fa[t],
D[fb[t], t] == -k2 fb[t] + k1 fa[t],
D[fc[t], t] == k2 fb[t],
fa[0] == 1,
fb[0] == 0,
fc[0] == 0
},
{fa, fb, fc},
t] // Flatten
fff[t_, k1_, k2_] := Evaluate[{fa[t], fb[t], fc[t]} /. sol]
Manipulate[
Plot[
Evaluate[fff[t, k1, k2]], {t, .00001, 10},
PlotStyle -> {Red, Blue, Black}],
{k1, 0, 3}, {k2, .00002, 3}]