Riggs' actual age has never been mentioned in the movie, nor in the sequels. Using clues in the movies we can conclude he is in his early thirties.
In an early draft of the script by Shane Black from January 86 it's said on the second page with the character descriptions that Riggs is 36 years old (thirty-six in August, says the script).
However, since Roger Murtaugh is in this very same draft of the script described as being 40 years old (and BTW not necessarily black as the description in the script doesn't mention his skin color) and not - as the Murtaugh later in the movie - as 50 years old (and black), I think it's safe to say that the filmmakers didn't feel obliged to stick to the original descriptions by Shane Black very much and Riggs doesn't really have to be 36 in the movie, too.
Clues from the movie
There are a some hints in the movie, though, that can help - together with some real history - to make deductions about Riggs' age in the movie (not very accurately, but at least roughly).
As you already mentioned here Riggs says in the movie that he was 19 when he did that rifle shot in Laos. But since the secret war in Laos ended in 1973, this means Riggs can't have been born later than 1954, because if he had been born later it would have been impossible for him to make that shot in Laos at the age of 19.
There are also other hints in the movie that add to the assumption he can't have been born later than 1954.
Another hint is that Murtaugh mentions to Riggs that Riggs' file says he's worked for the Phoenix Program in Vietnam (in the "Nobody wants to work with me"-scene).
The Phoenix Program began in 1967 and ended in 1973. So Riggs' can't have worked for the Phoenix Program longer than until 1973.
And from Victoria Lynn's headstone shown in the movie we know that Riggs' wife lived from 1953 to 1984.
With the additional information that Riggs has been married 11 years as the police psychologist tells Captain Murphy when they talk about Riggs' psychotic behavior, one can calculate that Riggs must have married his wife in 1973.
And since it's likely that he has met and married his wife in America (and not in Vietnam) this means that Riggs had returned from the Vietnam war either already before 1973 or at the very latest in (early) 1973.
All this hints together imply that Riggs must have been born 1954 or sooner.
And since the movie's events are likely meant to take place in December 1986 (because Black wrote the script in 1986 and principal photography of the movie also started already in August 1986, see Wikipedia) this means Riggs must have been at least 32 or older during the events of the first movie.
But how much older could he have been? There are also some hints in the movie that can help to make a deduction.
When Riggs is captured by General McAllister at the Dry Lake in Victorville, Riggs says (to McAllister) that he ran into some of that "Shadow Company pussies" in Saigon in 69. Which means that Riggs has served in Vietnam already in 1969.
It's not said in the movie how old Riggs was in 1969, but from the knowledge that it was legally possible to volunteer for service in the Vietnam war at the age of 17 (illegally already at younger age, as a matter of fact the youngest American KIA of the Vietnam war, Dan Bullock, was only 15, see Wikipedia) one could assume that Riggs was probably at least 17 in 1969. Or born not later than 1952.
But: if Riggs took illegal measures to get recruited and serve as a volunteer in Vietnam already at younger age, for example by faking his birth certificate (as the above mentioned Dan Bullock did), then Riggs could have been even younger than 17 in 1969, of course.
But still not younger than 15, because of the shot he did in Laos at the age of 19 (which can't have happened after 1973) and because it's not known that any American boys younger than 15 have served in Vietnam.
The last hint about Riggs' age in the movie is Murtaugh's angry remark that he was already driving before Riggs was an itch in his daddy's pants (i.e. before Riggs was born). If one assumes that Murtaugh got his driver's licence with 16, this would mean that Murtaugh must have been at least 16 years older than Riggs in the movie.
So when Murtaugh turned 50 in December 1986 (which means Murtaugh was born in December 1936), then Riggs can't have been born before 1952 (only later).
So I'd say Riggs was born either 1952, 1953 or 1954 (but 1953 or 1954 only if he's messed with his birth date at the recruiting office, so he could volunteer to serve (illegally) already in 1969 in Vietnam), which would make him in the movie either 34, 33 or 32 years old (by events in December 1986).