I've got this problem. I recently bought a flexible dip pen to practise copperplate, but it releases awful amounts of ink while flexed, which has two effects: The pen dries quite quickly and much more worse - it feathers and bleeds all over the place. It's so bad that I can't even actually see how the letters look, so I have no idea what I wrote.

Is there anything I could do? Using thicker ink and higher grade paper came to my mind, but I wonder if there is anything more I could do besides that.

What ink are you using? The only FP ink that doesn't feather for me is Noodlers Bulletproof Black.

I tried Pelikan Brown and Diamine Imperial Blue. Quite thin, I know. I just wondered if there was any other advice except for the really obvious two.

If I'm stating the obvious here, I apologize in advance, but the most likely cause is the angle of the nib to paper as described here. With the nib set properly in the holder, I can dip fully without the risk of a flood.

http://www.iampeth.com/lessons/getting_sta...ing_oblique.pdf

If you're using fountain pen ink, it will likely dump all the ink right on the paper as soon as you spread the point a bit. This is because fountain pen ink is not very viscous. You could try other kinds of ink or adding gum arabic to thicken it. Of course, I wouldn't recommend putting ink mixed with gum arabic into a fountain pen. In terms of other inks, just about anything works. I personally like Sumi and India, but there are tons of options. Just remember to add gum arabic to thicken, water to thin out.

EDIT - Reading the OP fully really helps. Um, sorry for pointing out the obvious.

Have you overcome your flow problem yet?

I recently tried Hunt 101 nibs for the first time, and am very pleased with the results. They hold a lot of ink and flex easily - also, they are very smooth writers. I used one for the video "Spencerian"in combination with Higgins Eternal ink, and Kodak Bright White inkjet paper.

For flex-nib writing, this combination is the smoothest I've found, to date.

Ken

p.s. Hunt 101 nibs and Higgins Eternal ink also work well on Viking Imperial and Character Original papers.

Not yet, I sort of put it to rest until I'd be able to get myself better paper and ink

I don't know what's available in the Czech Republic, but I have had excellent luck with my "Calli" calligrapher's inks with my dip pens.

I tried india ink, but without any success... I think the problem is in the paper I use.

Well the feathering sounds almost certain to be the paper so I would experiment with different paper and see what happens. It is important to note pen to paper angle as Caliken has mentioned as that can make a huge difference.
I have tried using Pelikan black with a flexible dip pen before and it was failure, I also have tried India ink without great success. As someone has mentioned this is most likely due to viscosity, it is simply too low meaning the ink is all too ready to flow off of the pen. An absorbent paper does not help with the viscosity problem either as it has a tendency to soak ink up.
Iron Gall ink is a brilliant ink for neat work but for general purpose and practice etc I don't find it ideal.
For an easy to use ink with flex nibs and broad nibs alike I love using Ziller Ink, the black is a Carbon based lettering ink and it lays down a nice strong visible line (I believe Higgins Eternal is a very similar ink). The one difficulty with such an ink however is that it is more liable to evaporate and need fine tuning than fountain pen ink does and this fine tuning requires a fair amount of trial and error to learn (though that is part of the fun ). Ziller also make various other inter-mixable colours. So really the two best inks for flex I am recommend are thick pigment based inks and iron gall (both as you probably know are unsuitable for fountain pens). Just so you know pigment based inks need frequent stirring but never stir iron gall.
One other thing I find is that I get better results if I load the ink on to the underside of the pen with my stirring stick and then touch the excess ink off on to the side of the inkwell, that way there is not too much ink on the pen at one time and I don't get ink all over the upper surface.