Does avoiding meat and fat for several days before a blood test for triglycerides make much difference in the results?

No. However, if you or your doctor actually care what you baseline serum triglycerides are, it is best to have the test done while you are fasting, before breakfast. There's disagreement whether "high serum triglycerides" is an independent risk for anything, or something that needs to be addressed in isolation.
Sugar. Triglycerides go up with sugar, carbohydrates - so if you lower your calorie by carbs/sugar it will go down. The supplement that helps lower triglycerides is carnitine need 2gm/day.