Join Date: Oct 2013
Location: Chilliwack, BC, Canada
Pull the fuel hose from the carb and put it into a container. Open the petcock and make sure that it will flow a couple of cups full in a minute. If it doesn't continue to flow, there's your problem, petcock.
If it does flow well, reconnect the fuel hose to the carb. and open the bowl drain to make sure that it will continue to flow for a couple of minutes. It needs to flow more than the engine can use but it's not a big requirement under low power.
If it doesn't continue to flow, there's a blockage in the carb fuel inlet or needle & seat.
If it flows well from the bowl, drain, you will need to remove the plastic choke "nut" so it doesn't break, then swing the carb bowl to the right side and pull the screws to drop the bowl and check for blockage.
That's how I would proceed.
As for inline filter: some have had success but be advised that the KLR has a very low fuel head (fuel level above the carb) so not much pressure to move fuel through the filter. Likely best to avoid a paper filter in favor of a screen or sintered metal filter.
The fuel outlet has a decent screen which works well enough for most people.
I recommend that you get this problem sorted before adding the variable of another such as the filter.
Diaphragm kits are available rather than replacing the automatic vacuum petcock.