Is there a word for a younger aunt or uncle?

An uncle or an aunt who are younger than their nieces or nephews are called uncle and aunt. The terms are not based on age but on parental relationships:

• the ​brother of someone's ​mother or ​father, or the ​husband of someone's ​aunt or uncle:

(Cambridge Dictionary)

In English, relationships are based purely on family lineage and gender of the person. Some languages distinguish on other features, for example:

• In Swedish, mother's mother is mormor; father's mother is farmor. In English, both are grandmother.
• In Thai, elder brother is pêe; younger brother is nóng. In English, both are brother.

So to directly answer your question, such people are simply aunt/uncle/niece/nephew.

In an informal context, many people would refer to an uncle who is approximately their age as a cousin. While it's strictly incorrect, you don't need to explain your family history to everyone you have a casual interaction with. If someone challenges this, they are your "zeroth cousin once removed" (thanks Wossname!)

I remember a children's story from my childhood where the protagonist referred to his mother's sister (younger than him) as his "pocket aunt." Unfortunately I cannot find any attestation on the internet other than one Reddit link, so this usage cannot be considered particularly common.

"Younger uncle" is probably your best bet. Just as you might say "younger brother" to mean a brother who is younger than yourself (as opposed to a brother who is younger than your other brother).

There are languages (e.g. Chinese), where you use a separate word for the same genetic association based on age (e.g. 妹妹 vs 姐姐), but English does not do that.

Let's start off by saying a maternal or paternal uncle is just called an uncle. An uncle is also the husband of your mother's or father's sister, so he is is not always consanguineous. And it doesn't matter how old that uncle is or their order of birth in the family, in today's English he is an ‘uncle’.

What's more, there isn't an English diminutive suffix that modifies the noun uncle. For example, in Italian a zio can be called affectionately zietto, not so in English.

Looking at its etymology we find that uncle is derived from Latin avunculus (a mother's brother) and its literal meaning was “little grandfather”, the diminutive of avus “grandfather”. Over time it ousted the Middle English terms eam (maternal uncle) and fædera (paternal uncle).

Therefore, uncle originally meant a ‘younger grandfather’, which indicates that 2,600 years ago there wasn't a specific Latin term for this male relative, the Latin speaking population just added a diminutive suffix to a pre-existing word.

The only alternative soluton that comes to mind is baby uncle. This works if the uncle is either younger or closer in age to his nephews and nieces. In fact, younger children are often called baby sister and baby brother by their elder siblings.

Examples from the net:

• My mother's baby brother fixed me up for my graduation. I looked real nice. After my graduation, we went out to eat and my baby uncle drove me around and made me countless drinks to celebrate.
  Source

• Most of my family is in Chicago. My baby uncle definitely has his points and truth about our family, but I believe we can all get along to a certain extinct. My family really don't have any major issues, it's just that everyone is so petty. I pray every night that my family will grow up ...
  Source

From an article titled My baby Uncle, Ding

• Alfredo Roces is the youngest of the Roces-Reyes brood of nine boys. Too close to his age, we, his older nieces—Sylvia, only six years younger, Ninit and myself, eight years—couldn’t bring ourselves to call him “Uncle” or “Tito,” only “Ding.”
  Source

Likewise, the term aunt is also derived from Latin, and there are no terms for a mother's sister, a father's sister, or an “aunt-in-law”.

c. 1300, from Anglo-French aunte, Old French ante (Modern French tante, from a 13c. variant), from Latin amita "paternal aunt" diminutive of *amma a baby-talk word for "mother" (cognates: Greek amma "mother," Old Norse amma "grandmother,"...
Source: Etymonline

But contrary to uncle there is the diminutive form auntie or aunty which dates back to 1787. However, it is a term of endearment and is not confined to a person's age or order of birth.

"Younger uncle", as others have suggested, would more probably convey that of your two uncles, he's the younger. I would not expect it to be interpreted relative to yourself.

I've known several cases of this, and they've always been introduced in a full sentence, like "He's actually my uncle, even though he's younger than me".