What is the pronunciation of English word feeling in General American accent? The normal sound [ˈfilɪŋ] or double the "l" sound, [ˈfiɫ lɪŋ] ?
The thing you call "double l" is more generally known as "dark l", and this topic has been researched (inconclusively) for decades. The classic study of the question is Sproat & Fujimura 1993 "Allophonic variation in English /l/ and its implications for phonetic implementation". One problem is that there isn't a well-defined and obvious boundary between dark and clear instances of /l/. It is now understood that there is a continuum of "darkness" realizations, dependent on context. The context for "feeling" is more on the "light l" side, although bear in mind that this is derived from "feel" which is on the dark side of "l". This paper by Yuan & Liberman proposes a way of quantifying darkness, but does not address the specific word or similar words.
Phonological considerations favor a "short" interpretation of /l/, in case you are hoping to look at duration and not darkness. A single intervocalic consonant phoneme immediately after a stressed lax vowel tends to get lengthened a bit, the rationale often being that stressed syllables in English cannot be just CV. This predicts a difference between "feeling" [fɪjlɪŋ] versus "filling" [fɪlˑɪŋ]. Consonant duration is not categorial in English, so as with darkness, the choice is not between "short" and "long", it is a continuum ranging from "shorter" to "longer".
I would say it [ˈfiː.lɪŋ]. (Source: native GA speaker.)
However, there's considerable variation within GA, and the only way to really be sure would be to record a lot of people saying the word several times, then look at the length of the [l] in the spectrograms, and compare it to the length of a reference "short" [l] in another word.