Venting a portable AC hose through a basement window can be done by making some modifications. You cannot use a dryer vent opening because it will be too small for the air conditioning vent hose. Use Plexiglas if you want the light and view to come through the window. Styrofoam is another option that is quick and inexpensive to use.
Do not vent a portable air conditioner out of a basement window in a dryer vent opening. The average dryer vent is four inches and the average air conditioning vent is five inches so it will not fit. Even though the vent hose is flexible, scrunching it into the dryer vent opening will not allow the venting system to work as it should. The air conditioning air flow is not as strong as a dryer's air stream, so it will not open any hatches that a dryer's air pushes open during operation. This would not allow the air conditioner to vent, possibly breaking the unit.
The portable air conditioner needs a venting system made for its specifications. Unfortunately they do not offer venting kits for basement or casement windows. You must devise a safe way to do this yourself.
Vent your hose through a piece of Plexiglas that you have installed in your window. Simply take the measurements of the glass in your basement window and get a piece of Plexiglas cut to its size at a local hardware or glass store. Ask them to cut a hole for the size of your air conditioner's vent hose off to one side of the Plexiglas panel. Bring the vent hose with you to guard against any mistakes in cutting the correct size hole.
It is not recommended the venting hose be extended for a portable air conditioner, in fact it may void out your warranty if you do so. For this reason you will need to bring the unit close to the window, which may mean preparing a pedestal of some type to lift the unit so the venting hose will reach the window. Keep all this in mind before picking out the place for the hole to be drilled in the Plexiglas. Even a few inches one way or another can make it too far away for the hose to reach, so do the preplanning of where everything will be placed before having a hole drilled.
Use Styrofoam as a replacement for your window glass if cutting off the outside light and view is not something you mind. Styrofoam is very flexible and it is something you can cut yourself. This is easier to work with than Plexiglas and also less expensive. Styrofoam also offers more insulation, which will help in keeping the cooler air in your basement. Remove your basement window glass and cut a piece of Styrofoam to the exact size of the glass panel. Cut the hole for the vent by tracing the vent hose opening on the material first. Put a few beads of window caulking along the sides of the Styrofoam and wedge it into the window opening. Put your vent hose through the hole, you can always shave some Styrofoam off if the hose does not fit, so it is better for it to be cut on the smaller side rather than larger.
Basement windows that open by pushing out from the bottom can be fitted for the vent while in the open position. Use a piece of Styrofoam with the vent hose opening already cut, to wedge between the bottom of the open window and the window sill. The Styrofoam piece will be at an angle.