You can consider gumbo the perfect representation of Louisiana culture as it is a mixture of African, European, and Native American cuisines. Gumbo is the dish most often associated with file powder. If you want an authentic Louisiana gumbo experience, you are going to want to use gumbo file powder or find an alternative that is equally traditional. The need to find a replacement is especially great given the fact that file powder is not always easy to find in brick and mortar grocery stores. The fact that there are equally traditional alternatives makes things easier. Consider the gumbo file powder alternatives below.
Your best bet: Okra
Traditional gumbo is made with one of two thickeners—gumbo file powder or okra. Many consider okra to be the more traditional thickener of the two since many historians believe the roots of the dish to lie mainly in West African culinary tradition. In Louisiana, it is likely that okra was used only during the warmer seasons when it was available and file powder used the rest of the time. In other words, okra gumbo would be a summer dish and file gumbo a winter dish.
Okra pods release a soluble fiber called mucilage that can make them seem slimy, especially if they are overcooked. It is this mucilage that will thicken your dish.
There is no real formula for how much okra to add to gumbo or other dishes when replacing file powder. You simply add the chopped pods until your dish achieves the desired degree of thickness. The consistency is a matter of taste. The main difference between file gumbo and gumbo with okra will be that okra gumbo will not have the distinctive flavor that file powder brings. Okra is more for the texture; its flavor is somewhat delicate.
A decent second choice: Roux
Roux is another thickener common throughout Cajun cuisine and that is sometimes used in gumbos. A roux consists of wheat flour fried in fat and can range in color from a light tan to a deep coffee color depending on how long the flour has been fried. Like gumbo file powder, it gives the dish a discernible flavor that is difficult to replicate with anything else. You can use a roux alongside either of the other two traditional thickeners. It is possible to use all three together, though this combination is decidedly non-traditional.
When roux is used in gumbo, it is traditional to use a medium-brown version. This can give the dish an attractive reddish color.
In a pinch: Corn starch
Corn starch is a neutral-tasting thickener made from the endosperm of the corn kernel. Despite the fact that it is virtually tasteless, corn starch is a good file powder substitute because of its thickening ability. It is a good alternative if you want to avoid the texture of okra or the high-fat content of roux. Simply make a slurry by mixing the corn starch with water and adding it towards the end of cooking. Since corn starch may dilute the overall flavor, it is a good idea to increase the quantities of spices and other flavorful ingredients.
Other alternatives
Root beer can provide the flavor that you would get from gumbo file powder. Of course, root beer by itself will not provide any thickening so you should consider using it alongside your cornstarch or roux.