I don't have a big jar to put my flour in so it's hard to measure by volume (you have to fluff the flour, pour it into a cup and then remove the excess - which cant be done outside of the original bag).
It it okay to just look up the conversion (for example, 1 cup of flour is 120 grams) and use that?
Short answer: YES. Measuring by weight is actually the better way to measure flour.
In fact, measuring flour by weight is the preferred method of measuring it in most places. This is because while measuring by volume is more convenient*, measuring by weight is more accurate. If you weigh your flour, however, you will always know you are using the same amount, whereas two individually measured cups of flour (done by volume) can have wildly different weights. This makes recipes where you measure by volume much harder to repeat reliably and perfect with small tweaks.
For a more detailed reference on converting cups of flour to grams, see this answer. As noted in the answers to that question and in the comments below, the average weight of a cup of flour can vary greatly, between 4 and 5 ounces (about 110 to 140 grams), though a heavily packed cup could weigh much more. I personally use 1 cup = 4.5 ounces (125 grams) when I need to convert from volume to weight, but your results may vary depending on the recipe you're using
*There seems to be some contention here. I'm from the US, where most people don't have kitchen scales (I'm the only one I know who does, despite being friends with lots of foodies). For us, measuring by volume is practically mandatory, and if I want to measure something by weight, I have to convert the measures myself since they're usually given as volume only. In other parts of the world, the situation is exactly the opposite -- everyone has scales, cups are nowhere to be found. Convenience is obviously relative.
In general, yes, you can absolutely weigh your flour (and other baking ingredients), and indeed should whenever possible.
There's an important caveat, however.
Weighing your ingredients produces more consistent results when reproducing a recipe. This is because measuring cups are not precision tools; there is variation in size from model to model. Bakers' techniques for filling them also vary. Indeed, the amount of flour can vary from scoop to scoop even for the same person.
When you weigh the ingredient, you eliminate two key variables: (primarily) the amount of air that ends up in the scoop, and the variations in size of measuring cups (grams don't change unless you change planets or your scale is broken). You also avoid simple differences in judgement of how full the scoop is.
Now, the caveat that emerges from this: when you make a recipe whose ingredients are measured by volume, you have to contend with this imprecision. The recipe writer's "1 cup" might be a cup minus a tablespoon by your measure. You've probably had the experience of a recipe coming out poorly the first time, and tweaking the ingredients next time. This is you compensating for the difference between the recipe author's equipment and technique and your own.
This problem does not go away if you switch directly to using weight. (In fact it might be exacerbated.) Since the recipe author did not give you weight, what was written down as "1 cup" might not be that standard 120g. It might be 128g, or 108g. While you are on the road to better reproducibility of the recipe, you likely still face a few rounds of trial and error.
You must measure the flour by weight to have any repeatable result. The more "technical" bakers (e.g., professionals, or also hobbyists who are into baking bread, where this really matters a lot) do this anyways. Also, using "cups" (i.e., volume) for everything seems to be a predominantly american thing, anyways, as far as I can tell.
Experiment: put flour in a jar, and ram it down with a big spoon. This will show you how much of its volume you can reduce, just by packing the grains of flour more tightly. I did this once when I had to store the amount contained in standard flour packages in a too-small container, and while I did not measure it, I'd say I got up to 25% less volume by ramming it down really hard.
