This short appears to be a parody of the 1922 movie "Under Two Flags", rather than of Foreign Legion movies in general.
First of all, Laurel did many of obvious parodies of famous movies during this time, such as "Mud and Sand", "When Knights Were Cold", etc. Second of all, there are no inter-titles explaining the plot or with dialogue. This is unusual, and to me it suggests that viewers were expected not to need inter-titles to understand what was going on, which further supports the idea that this was a parody of a specific and well-known movie.
Since the parody shorts all seemed to be puns on the names of the originals, I thought about what "Under Two Jags" could be based on and guessed the possibility "Under Two Flags". Searching for a movie with that name here on the IMDb, I found "Under Two Flags" (1922). The plot description for that movie matches the action in this short. It was also released not long before "Under Two Jags" was made, which I think confirms that it is the source of the parody.
The problem with parody if that if you aren't familiar with the original, the parody isn't very funny. The 1922 version of "Under Two Flags" is not available on DVD or VHS, but does not seem to be lost, since one person here on the IMDb has given it an unfavorable rating. It was remade in 1936 with Ronald Coleman and Claudette Colbert. Luckily, this version is available on DVD, though it is out of print on Amanzon.com. I would advise watching that movie before watching this short.
First of all, Laurel did many of obvious parodies of famous movies during this time, such as "Mud and Sand", "When Knights Were Cold", etc. Second of all, there are no inter-titles explaining the plot or with dialogue. This is unusual, and to me it suggests that viewers were expected not to need inter-titles to understand what was going on, which further supports the idea that this was a parody of a specific and well-known movie.
Since the parody shorts all seemed to be puns on the names of the originals, I thought about what "Under Two Jags" could be based on and guessed the possibility "Under Two Flags". Searching for a movie with that name here on the IMDb, I found "Under Two Flags" (1922). The plot description for that movie matches the action in this short. It was also released not long before "Under Two Jags" was made, which I think confirms that it is the source of the parody.
The problem with parody if that if you aren't familiar with the original, the parody isn't very funny. The 1922 version of "Under Two Flags" is not available on DVD or VHS, but does not seem to be lost, since one person here on the IMDb has given it an unfavorable rating. It was remade in 1936 with Ronald Coleman and Claudette Colbert. Luckily, this version is available on DVD, though it is out of print on Amanzon.com. I would advise watching that movie before watching this short.