No, and Harry will probably already have a dukedom at the time and it would be unusual for him to be given another. (Also, Charles is a little more than a decade older than Andrew, so it’s more likely than not that Harry will be the king’s brother when Andrew dies.)
Not every second son has gotten it. Queen Victoria’s second son was Duke of Edinburgh, and she eventually made her eldest son’s second son the Duke of York.
There being two, there is a pattern. The other is the Duchy of Lancaster, which makes the monarch Duke (or Duchess) of Lancaster, and pays the monarchy a private income… it goes into the privvy fund.
So the pattern is that 100% of Duchies in the UK have a member of the royal family as Duke (and/or Duchess) and receiving income from it.
More generally the rule is that the the Duchies all got subsumed into the Crown Estate
The Duchy of Lancaster is held by the crown, but the monarch is not and cannot be a duke. “Duke of Lancaster” is something the Queen is called informally, not an actual official title she holds.
A bit more complicated than that. There are two collections of historic inheritances, the Duchies of Lancaster and Cornwall, that come within the purview of the Crown. For the purposes of financial management, Lancaster is rolled up into the Crown Estates, from which part of the income goes to paying for “Head of State” expenses, but the bulk of it goes into the Treasury for general government expenditure. By tradition, Cornwall runs independently to provide income to the heir apparent, and AFAIK operates as a number of businesses under ordinary commercial rules.
There are other titles of Duke that by custom and practice are given to royal offspring, which can in turn be inherited, but don’t necessarily come with any land or wealth attached specifically to them.
There are Dukes from completely different families, whose titles may or may not be accompanied by holdings organised through a legal entity known as the Duchy of X. Some of the latter are extremely large and successful (Westminster), others may not be.
The Duchy of Lancaster is managed separately from the Crown Estate, and provides the Queen with an income (although a lot of it does get used for official-ish expenditures). None of it goes into the Treasury except, I guess, what the Queen voluntarily pays in tax.
The Sovereign Grant, which is based on the profits of the Crown Estate, is separate and is for purely official expenses.
Wait so even though there are 27 dukes there are only 2 duchys?
Pretty much. It looks like there are 30 dukes holding 35 ducal titles between them (some have more than one, e.g. the Duke of Richmond is also the Duke of Gordon and Duke of Lennox).
And of the two duchies, Lancaster hasn’t actually had a duke since 1413.
At this point it is traditional to recall that during the English Civil War, the city of Bristol was defended with breastworks.
There are some noble titles whose links to the geographical area their title claims to be ‘of’ part of their title is very limited. I’m descended from the baronets of [a city in India], the connection to that city is that the first baronet received his title for his activities whilst working out there with the East India Company, but after receiving the title all connections to that place ceased and the family became (and still are) strongly connected with a village in Devon.
And there’s apparently never been a Duchess of Lancaster, regardless of the monarch’s sex: Duke of Lancaster - Wikipedia