Is it possible to reduce nose flares without making a change to the nostril size?

You can reduce flare without size reduction with external wedge resection of the nostrils. While these incisions have a potential for visibility, they usually heal well after a few months. Thicker skin may take longer to color blend. The incision line should be placed as close as possible to but not in the natural nostril crease. 

It is important to evaluate your case in person, or with some photos, just to have an idea about the thickness of the ala, the size of the nostrils, the position of the nostrils, etc. In patients who have a thick ala, the nostril base reduction will not correct that, maybe a wedge alar resection can reduce some of the excess of thickness, and another technique is removing some of the skin in the rim of the ala, but the scars from those procedures should be explain to the patient, so he or she know about the resultant scars and how much improvement to expect.

dear renozIt is possible to reduce the alar flare by using bilateral lateral alar struts, flattening the curve of the ala without changing the base width or overall nostril size. Look for an experienced and well trained plastic surgeon certified by the American Board of Plastic surgery. See more than one consult.  Make a well informed decision. 

Without photographs we are guessing.  Having said that, if the nostril opening are small but the skin is thick there are a few ways of helping this. Excision in the crease will tend to flatten the nostrils , destroying the natural curvature but occasionally works ok. Internal excision of the muscles and fibro fatty tissue within the nostril itself is very tricky because symmetry is difficult and scarring internally can create deformities.