As this is a thing most conlangers fear i thought I could make a blog post about my thoughts on it with additional input.
Some think a kitchen sink language (KSL) is a conlang with just alot of features in it and have loads of various sounds.
That cannot possibly be it because there are loads of languages with lots of wierd things stuck togather into what could be considered a mess but have an inherent structure in the language. Same goes with sounds, there are natural languages with tons of consonants and tons of vowels again seemingly randomly put togather. And most certainly none of us conlangers would in their sane mind call a perfectly natural language a KSL now would we? Of course not, thats absurd. Going to a native speaker and say "youre language is a kitchen sink mess, change it" is more of a joke than anything else.
I would say the key differens between real languages or feature rich languages (or sound rich) and a KSL is structure and limitations. A KSL can contain nearly no limitations or barely have any at all, anything might be expressed in the most complicated of arrays in loops and dloops without perhaps anything really limiting it. Usually a language in real life have some form of limitations that removes a large portion of what we european people consider a natural choice on sentence construction, we do the same in some ways relative to other languages too as ours arent the perfect language construction and merely just one of many.
If one incorperate structure into the conlang, where things make sense perhaps culturally, historicly but mostly importantly semanticly, pregmanticly and my personal point of importans, grammar. throwing it all togather into a random mess where structure on all 3 levels are a kitchen sink while having a sensable structure of huge, and i mean really HUGE, tables like Basques half a million ways to declinate its nouns is perfectly fine, but again notice the structure must be sensable well thought through and more.
Same goes with sounds, the structure here is most importantly. Zompist in his LCK book gave an advice for phonology that i would find invaluable in this context and it shortly went as "Add or remove entire sound classes". In that way you are are having a structure because entire groups will show a sound structure, hebrew for example got a rather good fetish for many back throat sounds, perhaps your language enjoys various thrills, fricatives, fronted sounds etc. They are all a form of structure to be taken or removed and used.
Does this mean you must have PERFECT inflectional tables or sound system? Of course not, while a complete perfect system screams too much it is artificial holes, randomness, irregularities and more will make it realistic too, a personal tip is an over all structure, internal minor randomness and a few off shots that makes no sense what so ever (languages accumilate lots of dirt as time passes)
Dont fear complexity either because that doesnt make a kitchen sink either, it is threatening of it because its easy getting into the KSL trap there but if you work aorund the many loopiloops it might be entirely realistic and pleasent looking at (the pleasentness depends on the beholder).
But a thing to fear in this would be more lack of constrains of anyway, if there are things that can be expressed in tons of ways without limited structure you have a kitchen sink. real languages have forbidden constructions of a sentence that cannot be possible allowed, this differ between languages greatly but a great way to take a step from KSL is to create a form of limitation and a way to go around it. Instead of having genitives to say "my house" perhaps you could do like some american languages do and say "Houses me" as the house imposeses some form of feeling on you, take few things here and there and create limitations your language have that doesnt necciserly make sense. because english got non-sensical limitations aswell to other languages. You can do it on all levels, what is grammaticly plausible can be pragmatecly forbidden because thats just not how it is said. Japanese can express "Mr X is an american" but that just isnt right, they say "Mr X, He is an american". rather pointless little thing but gives a natural feeling and limits the language taking it a step from KSL.
I´ll finish this summery of my personal thoughts of this with a tip i heard on a forum in my conlang youth (perhaps infancy), "If you worry about making KSL and constantly quesiton yourself of it you are highly unlikely to ever make one". Good luck on conlanging!