How do I give my images this vintage travel photo effect?
You can shoot them properly exposed on a medium format camera with quality, low speed film. That's what this shot appears to be. If shooting digital you can use a camera with large pixels at low ISO and keep contrast and saturation under control. Expose properly when you take the photo. Do as little as is necessary in post. A scene such as this shouldn't take much, if any, post processing when properly shot.
It looks vintage because, like large format low speed film, there's very little noise/grain and good image detail.
Also like premium film, the color is vivid while being nowhere near as saturated as most digital cameras set to "Vivid" or "Eye-bleeding" color saturation. And don't even mention those who would try to create technicolor-ed rainbows of vomit using an HDR application to "enhance" this photo.
The same goes for contrast. There's not twice as much contrast as is needed. There's just enough. Kind of like properly developed and printed low speed film.
The photo has the "look" of one made with either a camera with large pixels or a camera with a larger than 35mm film negative. But at only 600x450 pixels, it is hard to tell. In the right hands today at that resolution, other than the shallow depth of field, it could have been taken using a phone with a decent camera. And the aspect ratio is 4:3 (most cameras with Four-Thirds and smaller sensors), not 3:2 (most FF and APS-C cameras). It could be a MF camera though. Or it might just be cropped.
If it was taken with a fairly long/narrow angle of view lens, the telephoto compression would distort the shape of the boat's hull at that angle. The lack of such distortion leads me to think it was made at a fairly normal focal length: one close to the diagonal length of the imaging sensor. If that is the case, then a wide aperture was also used. At 600x450 there's not enough detail to be sure, but the bow of the boat seems to be just a tad softer than the stern, so the depth of field looks fairly shallow.
The image was taken by National Geographic contributor Michael Melford. He began doing work for National Geographic in 1998 and started receiving feature assignments in 2003. Feature assignments for NatGeo usually meant being totally immersed in a project for months at a time.
His string of 13 features published in just over 7 years between 2005 and 2012 may have left little time for an assignment located on Dominica. None of his feature articles published during that span sent him to anywhere in the Caribbean where this was captured. That leads me to conjecture that this image could have been made during the 1998-2003 time frame when most of his assignments were for NG Traveler and may well have been captured using a 645 medium format film camera using either film (most likely) or an early digital back.
Based on this dated bio and this one on his facebook page, he shot mainly with Contex medium format film cameras until his first digital project in 2001 when he used a Contex 645 with a Kodak digital back to shoot The National Geographic Society's very first digital photo assignment. He later moved to the Canon EOS 1Ds which was in production from 2002 to 2004.
On the other hand, the earliest reference to this image on the web found using tineye is a 2008 National Geographic Traveler travel guide featuring the island of Dominica. However, the image has also been used as a file image for several various other travel guides published since by National Geographic and others. It may be possible the original print publication of the image was prior to the digital publication of National Geographic Traveler. The fact that the largest resolution of the image found by tineye is 600x450 supports the theory that it is a file image that existed prior to that usage.