Yes you could use a flash to get the same or similar effect. You would want to mount a diffuser on the flash to decrease contrast. A remote flash is always the best choice. You have the option of mounting it to your camera and also having it remote from the camera. Normally (especially in portraits) an on-camera flash is very non-flattering. A big bright light coming from the same angle of the lens is usually gonna look very unnatural. If you have a remote flash you can hold the flash unit off to the side and get a much better more natural look and you have more control of what shadows you're able to fill in.
If you only have the built-in flash.. you can try it but it will likely not look too great. Experiment, experiment, experiment.
Instead of a flash you could get something as inexpensive as a few sheets of white posterboard to reflect the sunlight in to the dark areas. White posterboard can work wonders. You can also back cardboard in aluminum foil but with direct sunlight you will often get a warm/orange cast. The white will also be softer and more diffused than aluminum foil.
I'd suggest trying some white posterboard for a few dollars before you go out and spend $200+ on a flash unit
a fill flash will definitely help with the shadows, but if you dont have another flash to use, im pretty sure a reflector would help too. i have a friend that uses a windshield reflector she bought at a dollar store. it works pretty well, and at $2 its cheap to replace, and to make different sized reflectors too.
Like I mentioned, the only problem with the silver reflectors (aluminum foil, car reflector things, etc) is that they will usually put a very warm/orange cast over the subject and won't look completely natural. The most natural look for working with direct sunlight is white whether it be a white sheet, a white posterboard, etc. You can experiment with the aluminum/silver/reflective materials and see what you get. From when I've found, it's just way too orange and honestly it's just too harsh. The white does a good job of balancing the light color and diffusing light.
If you're farmilliar with your aperture control try lowering it (opening it). This will give you less depth of field and will blur out the background slightly which will direct more attention to the subject of the photo (the people in the portrait). An in-focus distracting background usually isn't the best thing when dealing with portraits.
If you're not familiar with aperture settings and such yet, don't worry. You're doing fine. You'll learn all about that stuff in your upcoming classes.