we know Darboux theorem for highersymplectic geometry is not correct in general, but is there any Darboux like theorem for nondegenerate 3forms in 6manifolds?

This depends on what you mean by 'Darbouxlike'. It is certainly not true that a closed nondegenerate 3form on a 6manifold is necessarily locally equivalent to one of the 'flat' models, so there is no direct analog of the Darboux' theorem in this case. As I remark in my article "Remarks on the geometry of almost complex $6$manifolds" (Asian Journal of Mathematics 10 (2006), 561–606, also available on the arXiv as arXiv:math/0508428), the closed $3$forms of elliptic type in dimension $6$ essentially depend on 4 arbitrary functions of 6 variables (modulo diffeomorphism). However, there is an analog if you are willing to consider something stronger: If $\phi\in\mathcal{A}^3_+(M^6)$ is a $3$form of elliptic type on an oriented $6$manifold $M$, then there is a unique $J(\phi)\in\mathcal{A}^3_+(M^6)$ with the property that the complex $3$form $\Upsilon = \phi+i \ J(\phi)$ is decomposable and hence of type $(3,0)$ with respect to an almost complex structure $J_\phi$ on $M$ that induces the given orientation of $M$. All this is algebra. However, now, if one adds the hypothesis that $d\Upsilon = 0$, which is, of course, the same as $d\phi = d\bigl(J(\phi)\bigr)=0$, then one has that there always exist local complex functions $z^1,z^2,z^3$ such that $\Upsilon = dz^1\wedge dz^2\wedge dz^3$. In particular, $\phi = \mathrm{Re}(dz^1\wedge dz^2\wedge dz^3)$, so this is a sort of Darbouxlike theorem; it's just that you need more hypothesis than the closure of the original form. There is a similar result for nondegenerate $3$forms of hyperbolic type. This is the case in which the form $\phi$ can be written locally as $\phi = \phi_+ + \phi_$ where each of $\phi_\pm$ is decomposable while $\phi_+\wedge\phi_\not=0$. (These two summands are unique up to permutation.) In this case, the 'Darbouxlike' theorem is that $\phi$ can be put in normal form if and only if $d\phi_+=d\phi_=0$, which is stronger than $d\phi=0$ (which is not sufficient by itself). Finally, there is the case of nondegenerate $3$forms of what might be called 'nilpotent type' (which is not a stable type in Hitchin's sense, but is nondegenerate in the sense described by the OP). A $3$form $\phi$ on $M^6$ is nondegenerate of nilpotent type if and only if each point lies in some open set $U$ on which there exists a coframing $\omega^1,\ldots,\omega^6$ for which $$ \phi = \omega^4\wedge\omega^2\wedge\omega^3 +\omega^5\wedge\omega^3\wedge\omega^1 +\omega^6\wedge\omega^1\wedge\omega^2. $$ For such a $\phi$, the conditions that it can locally be put in this form with $\omega^i = dx^i$ for some coordinates $x = (x^1,\ldots,x^6)$ consist of two things: First, the condition $d\phi=0$, which is clearly necessary; second, the condition that $3$plane field $D\subset TM$ defined by $\omega^1=\omega^2=\omega^3=0$ (which is welldefined by $\phi$) should be Frobenius. It is not hard to show that these necessary conditions are also sufficient, so this is the 'Darbouxlike' normal form theorem in this case. Note the interesting fact that, in each of these three cases, the 'Darbouxlike' conditions are all first order equations on $\phi$. This does not continue in higher dimensions. In dimension $7$, the two stable types of $3$forms each have examples that are flat to first order but not flat to second order, so the 'Darbouxlike' theorems in this case turn out to involve a mixture of first and second order conditions. 

