"More thicker hair"? Is it correct to use 'more' with comparative adjectives?

The utterance is

This [wig] is made out of the Yaki synthetic hair, not the typical synthetic hair. And whenever, just FYI, whenever you guys are doing, um, characters with really thick hair such as Rapunzel, get Yaki synthetic hair because it looks so much more realistic [than other synthetic hair]: there's no shine whatsoever to it, um, and it's so much more thicker [than other synthetic hair]. Um, so I really, really, really, really recommend this.

The woman was 21 when the video was published, and she seems to be quite aware of what she is saying and not stumbling for words. That she uses a so-called double comparative ("much more thicker") with aplomb is evidence that the form is grammatical for her, whose usage is either an idiolect or based on a dialect. In spontaneous spoken speech it cannot be called "ungrammatical" for those for whom it is grammatical.

Briefly, yes I have heard (and read) other native speakers of English use double comparisons. A somewhat famous instance in written English is

Clara Basil is the most strangest person I know.

This sentence, which appeared in the US newspaper The Atlanta Constitution has been referred to in several studies of the usage of the "double comparative" in both British and American English. It is a feature of some people's language. In the dialect called current standard (written) English, it is an error. It seems dialectal in both the US and the UK.

This is called a double comparative (DC). While it is considered incorrect in Standard English, some dialects of American English use it:

According to Wlodarczyk (2007), it is associated with Appalachian English and African American Vernacular English (see also Montgomery 2008:267), though it may be found in other North American dialects as well, such as Newfoundland English (Clarke 2004:314).
_{Yale — Double comparatives}

It's entirely possible that the speaker finds double comparatives perfectly natural. It's also entirely possible that she simply made a mistake.

A little history:

The Wlodarczyk paper brings up some interesting information. It says that double comparatives were used a little in Old English, much more in Middle English, but in Shakespeare's time they were controversial:

As far as [Early Modern English] is concerned, particularly well known is the presence of DC in Shakespeare, (e.g., Blake 2001) and there is evidence that DC was a feature of high style (González-Díaz 2004: 192). For instance, in Ben Jonson’s 1640 English grammar, it is viewed as “imitating the manner of most ancientest and finest Grecians”. At the same time, however, other early modern grammarians (Greaves in 1594 and Butler in 1636) saw it as outdated or recommended its avoidance (Dons 2004: 56), indicating the decreasing acceptability of the form. DC was thus prevented from becoming part of standard English grammars by the standardisation-related preferences for uniformity of coding and economy.