I’m American, from the Midwest in particular and I always pronunced the word figure as ˈfi-gər. I rarely have gotten any comments on that, though I have gotten comments on a similarity to a Canadian accent, such as a relaxed about along with process with a long o, (but that’s for another time). It wasn’t until recently that some friends of mine started commenting on the way I say it. I haven’t done too much research, so is my pronunciation technically incorrect?
There are two pronunciations: fi-gyər and, like you pronounce, fi-gər. One is not more correct than the other, although the first pronunciation is more common. See here. Also, according to M-W, fi-gər is both a British and an American pronunciation. Personally, I say fi-gyər and I'm from New York.
A pronunciation can't be "technically incorrect", because pronunciation is not a technical matter. A common analogy used in linguistics for what "correctness" means in the context of language is clothing: we can say that it's "incorrect" to wear jogging clothes to an interview for a white-collar job, but this is because of social conventions/considerations, not because of any technical requirements. The definition of "correct" pronunciation is as much a matter of opinion as the definition of "correct" fashion.
The pronunciation of figure that rhymes with bigger has been criticized, especially in the context of American English:
In proper British speech, figure rhymes with bigger, but never so in educated American speech. "The British pronunciation is sometimes heard in AmE," says Burchfield (1996), "but is usually condemned as substandard."
(The Big Book of Beastly Mispronunciations, 2nd edition, by Charles Harrington Elster, 2005; p. 201)
The pronunciation with a palatal glide /j/ (like the sound that the letter "y" makes at the start of the word "yes") corresponds somewhat more regularly to the spelling, but this doesn't really prove anything about which pronunciation is "correct".
There are examples of words spelled with "u" that have undeniably irregular pronunciations: nobody claims it is "incorrect" to pronounce the noun minute without a palatal glide after the /n/.
Some historical context
As I mentioned in the previous section, the pronunciation with /j/ has a more regular correspondence with the spelling, and this was given some weight in the past by certain "orthoepists" or writers that were interested in prescribing "correct" pronunciation.
John Walker (an Englishman) wrote the following about the pronunciation of this word in his Critical Pronouncing Dictionary of 1791:
☞ There is a delicate and a coarse pronunciation of this word and its compounds. The first is such a pronunciation as makes the u short and shut, as if written figger : the last preserves the sound of u open, as if y were prefixed fig-yure. That this is the true sound of open u, see Principles, No. 8.
I'm not sure how exactly to interpret the meaning of Walker's terms "delicate" and "coarse" (my guess would be that he means the pronunciation figger was preferred in polite society ), but note that he seems to have a certain amount of bias towards the pronunciation with /j/ because of its regularity, describing it as "preserving" the "true sound" of the letter U.
There seems to have been some variability in the development of the "U" sound that was taken into English from French when this vowel occurred in an unstressed syllable. Although the "regular" pronunciations used in modern English mainly continue forms with glides, there is evidence for /j/-less pronunciations in a number of other words.
One example is creature: the /j/-less pronunciation survives in the dialectal form critter. The OED entry for creature says "The realization of the second syllable varied in Middle English and early modern English according to whether this syllable showed secondary stress; pronunciations of the type /ˈkriːtʃə/ ultimately reflect pronunciations with secondary stress, while pronunciations of the type /ˈkriːtə/ ultimately reflect pronunciations without such secondary stress. Compare forms at nature n., pasture n., etc."
The book English Pronunciation in the Eighteenth Century: Thomas Spence's Grand Repository of the English Language, by Joan C. Beal, has a more detailed description of the relevant sound changes. In chapter 5 ("The Phonology of Eighteenth-Century English: Evidence from Spence's *Grand Repository and Contemporary Pronouncing Dictionaries"), Beal says
“In unstressed syllables, alongside the development [of the vowel sound represented by the letter U] to /juː/, there existed a variant pronunciation with /ɪ/ or /ə/. Particularly before final /r/, evidence for this becomes increasingly common in the homophone lists of late seventeenth-century orthoepists, such as Cooper (1687), who has, for example, centaury, century; ordure, order; pastor, pasture; and picture, pick’t her as homophones. In this context, the pronunciation with /ɪ/ or /ə/ is not stigmatized in the seventeenth century, but in other environments it is less common in the seventeenth century. Cooper gives scrupelous in his Latin text (1685) as ‘facilitas causa’, but in the English edition (1687) as ‘barbarous speaking’. As we move into the eighteenth century, though, criticism of the pronunciation /ɪr/ or /ər/ becomes more widespread: according to Sheldon (1938:275). ‘Swift ... writes creeter to indicate vulgar pronunciation’ in his Polite Conversations.