Are talking about flour (milled grain) in general or wheat flour specifically?
There are certainly non-wheat flours that can be used include (by not limited to): cornstarch, rice, arrowroot, tapioca, potato starch and others.
Dairy can be used, milk, cream, yogurt, cheeses among others.
There are also thickening agents such as agar, guar gum, xanthan gum, egg whites, gelatin, egg yolks, tomato puree, cooked potato, mustard (an emulsifier), lecithin amongst others.
In many cases, a specific dish may have thickeners that are more appropriate or work better than others, so it's difficult to make a recommendation without knowing the preparation that it is intended for.
Cornstarch, tapioca starch, Arrowroot (my favorite), pureed root vegetables, or a simple reduction of the sauce. Mustard or swirling butter in to emulsify also will thicken a sauce some. Tomato paste will also help. It really depends what the sauce is as to which method is the best.
Yes to Susan W suggestions.
Also depends on whether sauce is hot or cold.
Another emulsifier is egg yolk and, to a lesser extent, pureed silken tofu.
Last, for volume and smoothness, pureed cooked root vegetables.
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There are certainly non-wheat flours that can be used include (by not limited to): cornstarch, rice, arrowroot, tapioca, potato starch and others.
Dairy can be used, milk, cream, yogurt, cheeses among others.
There are also thickening agents such as agar, guar gum, xanthan gum, egg whites, gelatin, egg yolks, tomato puree, cooked potato, mustard (an emulsifier), lecithin amongst others.
In many cases, a specific dish may have thickeners that are more appropriate or work better than others, so it's difficult to make a recommendation without knowing the preparation that it is intended for.
Good luck.
Also depends on whether sauce is hot or cold.
Another emulsifier is egg yolk and, to a lesser extent, pureed silken tofu.
Last, for volume and smoothness, pureed cooked root vegetables.