Is it possible for me to get a straight line mini tummy tuck?

Although I cannot give you specific advice based on the limited photograph, most patients who present for abdominal wall contouring surgery do not do well with mini tummy tuck surgery.In my opinion, the mini tummy tuck is an operation that produces very limited results and is very rarely indicated. It involves a shorter incision but does not address the majority of the abdominal wall issues present for most patients who present consultation. For example, the area of skin excised is quite small. The abdominal wall musculature is addressed below the umbilicus leaving the upper number wall potentially lax. The appearance of the umbilicus is not necessarily addressed sufficiently.
For the vast majority of patients who have had pregnancies and/or weight loss a full abdominoplasty is necessary to achieve the desired results. 
 In our practice planning the incision line for tummy tuck surgery is done after careful communication of patients' goals and preferences. I find that marking patients the day before surgery, as much as possible, with the help of the patient's planned swimming suit or undergarment, helps when it comes to placement of incisions.
In most cases, the tummy tuck incision can be kept very low, usually at or below  the pubic hair line (or at or below an existing C-section scar).
The use of the progressive tension relieving suture technique (sutures placed between the abdominal wall flap and the underlying abdominal wall fascia) allows us to keep the resulting scar low and relieve some of the tension upon the tummy tuck closure.  Reducing tension upon the incision line helps keep scars as far as possible.
Sometimes, especially for patients with a relatively short torso and/or minimal redundant abdominal wall skin, a short vertical scar is necessary ( in addition to the usual transverse tummy tuck scar). This vertical scar results from closure of the previous umbilical opening and prevents excessive tension upon closer in the midline of the tummy tuck incision line. If this vertical incision is not used, patients may end up with high scars, wound healing problems and/or wider scars.
 Patients should keep in mind that the lower the incision line used for tummy tuck surgery, the less skin can be removed at or above the umbilicus.  This may be especially relevant for patients who have stretch marks and/or piercings above the umbilicus.  Sometimes, patients elect to have their incision lines placed higher so that more skin and/or an existing supra umbilical piercing can be removed  during the tummy tuck procedure. 
 Always best to communicate your goals, concerns, and questions directly with your plastic surgeon, who will be your best resource when it comes to specific thoughts and advice.
 Best wishes for an outcome that you will be very pleased with.

You can discuss your requests with your surgeon. Yes, the scar can be straight, but might be somewhat longer.