I'm not aware of any FAA-approved (or FAA-accepted) products for on-engine fuel injector cleaning. If your injectors are blocking due to lead deposits a tricresyl phosphate additive may help improve lead scavenging and prevent the problem, but it's probably not going to clean a clogged injector. (TCP is also pretty nasty stuff – leaning your engine more aggressively can often accomplish the same thing without the chemicals.)
Frankly 100LL is a pretty darn good solvent: it even dissolves that blue dye they put in it which nothing else ever seems to budge. If your injectors are blocked due to contamination that 100LL won't dissolve having your mechanic take them off and bench-clean them is probably a good idea (as Thomas pointed out this isn't rocket surgery - any competent mechanic should be able to do it without damaging anything).
As far as other "pour it into the gas" cleaning additive, as with many things There's an Advisory Circular that covers this (AC 20-24D) - at least to some extent: That Advisory Circular deals with fuel specifications for type certification of aircraft/engines/APUs, but it contains this interesting nugget:
(1) Fuel additives that are incorporated into ASTM, governmental or military specification, or other industry-based consensus organization specification, are considered to be identified in sufficient detail to be accepted by the FAA under existing operating limitations on TCs, amended TCs, STCs, or ASTCs, provided there are no changes to those operating limitations.
So if you can show that the injector-cleaner chemical you want to use is an approved additive according to ASTM D910 (the standard that governs 100LL avgas), your use of the additive is in accordance with the specification ("not more than X% or Yppm"), and the additive is not contraindicated by the manufacturer (of the engine, airframe, or any components) you should theoretically be OK to use it.
Navigating that legal morass is something you probably don't want to do though: The risks of getting it wrong are not just paperwork-related: some additives can damage your fuel system, or even lead to an engine failure.
A bench cleaning of your injectors is probably the easier and safer option.