My brother-in-law makes perfect gravy every time!! Here's what he does:
1. Heats the broth until very hot.
2. In a shaker (like the kind used to mix protein powder with juice or other liquid), he puts the flour and water and shakes vigorously. The shaker has a grid inside which helps to break up lumps. Alternately, you can put the flour and water in a bowl and use a whisk to mix until there are no lumps. Worst case, you can use a strainer.
3. Add a little bit of the flour/water mixture to the hot broth. Stir. Continue stirring. When it looks like it's all mixed in, add a little more flour/water mixture to the broth. Stir again. Keep stirring. Continue this process until the gravy is the consistency you want.
Remember that hot gravy will thicken upon standing.
He swears that the trick is to be patient when adding the flour/water mixture, not adding it all at once, and allowing time to stir the mixture thoroughly before adding more.