To my knowledge there have been no legal challenges on switchblade bans since the Heller v. DC decision. It is possible such a challenge could be made. In my opinion they wouldn't survive (see US v. Miller) because the courts probably would not find that a switchblade is not "arms" under the second amendment and thus any laws banning them would not be unconstitutional.
Held:
The Second Amendment protects an individual right to possess a
firearm unconnected with service in a militia, and to use that arm for
traditionally lawful purposes, such as self-defense within the home.
...
None of the Courts precedents forecloses the Courts interpretation.
Neither United States v. Cruikshank, 92 U. S. 542, 553, nor
Presser v. Illinois, 116 U. S. 252, 264265, refutes the individual rights
interpretation. United States v. Miller, 307 U. S. 174, does not
limit the right to keep and bear arms to militia purposes, but rather
limits the type of weapon to which the right applies to those used by
the militia, i.e., those in common use for lawful purposes.
Like most rights, the Second Amendment right is not unlimited.
It is not a right to keep and carry any weapon whatsoever in any
manner whatsoever and for whatever purpose: For example, concealed
weapons prohibitions have been upheld under the Amendment
or state analogues. The Courts opinion should not be taken to cast
doubt on longstanding prohibitions on the possession of firearms by
felons and the mentally ill, or laws forbidding the carrying of firearms
in sensitive places such as schools and government buildings, or
laws imposing conditions and qualifications on the commercial sale of
arms. Millers holding that the sorts of weapons protected are those
in common use at the time finds support in the historical tradition
of prohibiting the carrying of dangerous and unusual weapons.
The handgun ban and the trigger-lock requirement (as applied to
self-defense) violate the Second Amendment. The Districts total ban
on handgun possession in the home amounts to a prohibition on an
entire class of arms that Americans overwhelmingly choose for the
lawful purpose of self-defense. Under any of the standards of scrutiny
the Court has applied to enumerated constitutional rights, this
prohibitionin the place where the importance of the lawful defense
of self, family, and property is most acutewould fail constitutional
muster. Similarly, the requirement that any lawful firearm in the
home be disassembled or bound by a trigger lock makes it impossible
for citizens to use arms for the core lawful purpose of self-defense and
is hence unconstitutional.
Heller v. DC (2013)