In the case of the Second Amendment, the relevant courts, such as the U.S. Supreme Court in the District of Columbia v. Heller, 554 U.S. 570 (2008) case have held that the right is subject to reasonable regulation. In that case, Justice Scalia, writing for the majority stated:
Like most rights, the right secured by the Second Amendment is not
unlimited. From Blackstone through the 19th-century cases,
commentators and courts routinely explained that the right was not a
right to keep and carry any weapon whatsoever in any manner whatsoever
and for whatever purpose. See, e.g., Sheldon, in 5 Blume 346; Rawle
123; Pomeroy 152–153; Abbott 333. For example, the majority of the
19th-century courts to consider the question held that prohibitions on
carrying concealed weapons were lawful under the Second Amendment or
state analogues. See, e.g., State v. Chandler, 5 La. Ann., at 489–490;
Nunn v. State, 1 Ga., at 251; see generally 2 Kent *340, n. 2; The
American Students’ Blackstone 84, n. 11 (G. Chase ed. 1884). Although
we do not undertake an exhaustive historical analysis today of the
full scope of the Second Amendment, nothing in our opinion should be
taken to cast doubt on longstanding prohibitions on the possession of
firearms by felons and the mentally ill, or laws forbidding the
carrying of firearms in sensitive places such as schools and
government buildings, or laws imposing conditions and qualifications
on the commercial sale of arms.[Footnote 26]
We also recognize another important limitation on the right to keep
and carry arms. Miller said, as we have explained, that the sorts of
weapons protected were those “in common use at the time.” 307 U. S.,
at 179. We think that limitation is fairly supported by the historical
tradition of prohibiting the carrying of “dangerous and unusual
weapons.” See 4 Blackstone 148–149 (1769); 3 B. Wilson, Works of the
Honourable James Wilson 79 (1804); J. Dunlap, The New-York Justice 8
(1815); C. Humphreys, A Compendium of the Common Law in Force in
Kentucky 482 (1822); 1 W. Russell, A Treatise on Crimes and Indictable
Misdemeanors 271–272 (1831); H. Stephen, Summary of the Criminal Law
48 (1840); E. Lewis, An Abridgment of the Criminal Law of the United
States 64 (1847); F. Wharton, A Treatise on the Criminal Law of the
United States 726 (1852). See also State v. Langford, 10 N. C. 381,
383–384 (1824); O’Neill v. State, 16 Ala. 65, 67 (1849); English v.
State, 35 Tex. 473, 476 (1871); State v. Lanier, 71 N. C. 288, 289
It may be objected that if weapons that are most useful in military
service—M-16 rifles and the like—may be banned, then the Second
Amendment right is completely detached from the prefatory clause. But
as we have said, the conception of the militia at the time of the
Second Amendment’s ratification was the body of all citizens capable
of military service, who would bring the sorts of lawful weapons that
they possessed at home to militia duty. It may well be true today that
a militia, to be as effective as militias in the 18th century, would
require sophisticated arms that are highly unusual in society at
large. Indeed, it may be true that no amount of small arms could be
useful against modern-day bombers and tanks. But the fact that modern
developments have limited the degree of fit between the prefatory
clause and the protected right cannot change our interpretation of the
Footnote 26 in that passage states:
We identify these presumptively lawful regulatory measures only as
examples; our list does not purport to be exhaustive.
As noted in the comment by @phoog, and implied by the first paragraph of the Heller decision cited above, the Second Amendment makes no mention of age. Yet surely nobody believes that a two-year-old has a right to keep and bear arms. So there must be an implicit age limit, or at least a capacity to define one by statute, somewhere.
The notion of an "adult" for purposes other than voting, is not one expressly created or defined in the U.S. Constitution and can be defined in different ways for different purposes under the law. And, it is in many areas of the law.
For example, the drinking age is set by federal law as 21 (indirectly via ties to highway funding), while the age for smoking in most states is 18.
But, neither age has constitutional stature for purposes other than voting and prior to 1971, in the midst of the Vietnam War, when the 26th Amendment was adopted, the age 18 had no formal significance in the constitution. Indeed, Section 2 of the 14th Amendment to the United States Constitution ratified in 1868, the presumptive age of the franchise which if not followed would lead to a penalty for a state in apportionment, was 21 years of age.
Given that a state statute like the one passed in Florida can overcome another state statute, and that no federal law in place currently prohibits the imposition of this age limit; the absence of a constitutional limitation preventing a twenty-one year old age limit to buy guns means that the law is constitutional and valid.
This general conclusion is bolstered by case law specifically on point decided after Heller in the conservative 5th Circuit. On October 25, 2012, the Court of Appeals held in that case that the United States may ban federally licensed firearms dealers from selling handguns to people under age 21, in a similar suit brought by the National Rifle Association. The case was National Rifle Association of America Inc et al v. Bureau of Alcohol, Tobacco, Firearms, and Explosives et al, 700 F.3d 185 (5th Cir. 2012). The U.S. Supreme Court declined to review this decision.
This 5th Circuit decision isn't directly binding on Florida, which is not in the 5th Circuit, but it is powerfully persuasive authority. Indeed, this case has previously been cited as good law by an intermediate appellate court that is part of the state court system of Florida. Norman v. State, 159 So.3d 205 (Fla. App. 2015).
The NRA lawsuit will likely be dismissed as a result.
At some point an age limitation probably isn't reasonable and does infringe on the Second Amendment as articulated in Heller. If, for example, only people over the age of 70 years were allowed to possess firearms, the courts would probably strike down that regulation as unreasonable. But, that isn't the statute at issue right now, and it is very hard to see a permanent constitutional line being drawn at eighteen when a legislative body in its wisdom has chosen to draw that line at twenty-one, which is a time honored threshold for adulthood for many purposes.