Hi - you didn't say what steps you've already tried to improve the ink flow, so it's possible some of my suggestions are things you've already done, but here goes:
1. remove the ink cartridge or converter and flush the section (with the nib and feed still in place) thoroughly with cold water that has a tiny drop of dish detergent added. I use an "ear syringe" (Amazon or CVS) to force a lot of water through the section. Once the water flows through clear, I use "Fountain Pen Flush" in the syringe (don't throw it away, it's re-usable many times). I get my pen flush from Indy-Pen-Dance. Finally, flush with clean water. This should have blown out any crud built up in the fine channels of the feed.
2. Take the nib and feed out of the section, and reseat them making sure the breather hole and slit in the nib line up with the channels in the feed. Make sure to push them home fully - you should see the stud on the end of the feed show up inside the nipple that pushes into the ink cartridge. While they are out - use a 10x jewellers' loupe to inspect the channels to see they are clear. Inspect the slit in the nib to see it is clear and open all the way to the tip (it should be a very small slit, but not entirely closed.)
3. Throw away the ink cartridge that came with the kit. Nobody knows how long it's been sitting on the shelf, and it was cheap junk anyway.
4. Buy a bottle of decent quality ink and use a converter. Want blue ink? Waterman's Serenity Blue and Mysterious Blue are good. Pelikan 4001 Royal Blue is good. Want black ink? Again, Waterman's or Pelikan or Parker or Sheaffer are all good. Avoid the "heavily pigmented" inks, which by definition have more solids and less liquid. Avoid red ink - it's fun to write with, but not for a pen that has a tendency to dry up.
5. Make sure your cap seals. Usually the clip finial seals one end of the brass tube in the cap, and the screw threads at the other end seal against the barrel of the pen. If it isn't sealed, evaporation can cause the ink in the feed channels to dry up and it will eventually lead to clogs.
6. You didn't say if this is something the pen has done from the very start or if it developed over time. If it was always that way, the nib probably needs a little tuning. If it started out great but deteriorated, cleaning should have taken care of it.
7. Here's a link to Richard Binder's "
10 Commandments for Nib Tuning". You cannot get better advice than this, and it includes a link to the notes he gives to people who attend his nib smoothing/tuning workshops.
Good luck!