Check filter light flashing - dryer willnot start

I expect it has 4" duct exhausting to outside? It's possibly restricted with lint, either at the louvered opening, or in the pipe itself. Spiral plastic vent is particularly restrictive and captures more lint than smooth sheet metal pipe. A restricted exhaust/limited air flow will likely trigger a filter message.

Clean the lint filter

The CHECK VENT duct blockage sensing system detects and alerts you to blockages in the duct work that reduce exhaust flow from the dryer. This light does not indicate any problems with your dryer. If this light blinks, it indicates that your home's exhaust system/duct work has a serious restriction

Every time the dryer is turned on, the CHECK FILTER LIGHT WILL BLINK, as a reminder to make sure the filter is clean. Always make sure the lint filter is clean before starting a new load; a clogged lint filter will increase drying times.

The Kenmore Elite dryer has a sensor that detects poor exhaust venting, and when it does, a light flashes on the control panel. This warning light does not include a mechanism to stop gas flow, but if it is allowed to flash for an extended period, poor venting may cause the dryer to overheat. As a result, a fuse might blow and disable the gas valve or ignitor. You can prevent this by diagnosing the reason for the flashing indicator light as soon as possible.

In many cases, LINT has built up somewhere in the exhaust pipes.

Check under the lint filter. Pull it out,look inside the slot it fits in, and clear all lint from this area.

Is it possible you have used the WRONG VENT MATERIAL?
Check your vent to make sure it is 4 inch rigid or semi-rigid metal ducting. If your venting is plastic or flexible foil, replace it before using the dryer.

Check your vent hood outside. You may have a restricted or damaged vent hood. It must be clean and free of lint buildup. Check the damper and make sure it opens fully and easily and is free of lint.

I know you said you have no elbows, but I have posted the pipe run lengths with and without elbows. Keep in mind this is with 4 inch rigid or semi rigid metal ducting.

Measure the length of your exhaust system and count the elbows. Use the chart below to see if your duct is too long. If it is too long, have the duct routed to another location that is within the venting guidelines.

0~90 degree elbows=65 ft of 4 inch rigid metal duct.
1~90 degree elbow=55 ft of 4 inch rigid metal duct.
2~90 degree elbows=47 ft """"""""
3~90 degree elbows=36 ft """"""""
4~90 degree elbows=28 ft """"""""

You should always use duct tape or metal tape on all joints, NEVER USE SCREWS, as screws capture lint inside the pipe.

One more note. Lots of people overlook the fact that fabric softeners can build up on the lint filter over time. This buildup can restrict the airflow through the filter reducing dryer efficiency and lengthening drying times. After removing lint, if the filter looks dark or dirty when held up to the light, follow these steps to clean:

Use hot soapy water and a stiff brush to clean
the filter.
Make sure the filter is completely dry before
reinstalling it and using the dryer.
NEVER operate the dryer with a wet lint filter.

The unit is seeing a restriction in air flow disconnect the exhaust at base of machine turn to air dry or fluff you should get good air movement coming out of the exhaust I will assume the machine worked when new if flow is weak then there is lint in the blower air passage from the machine if good you will know the difference the the restriction is in the exhaust exiting the house on one occasion i did encounter a bad control if everything passes the test an dryer is operating correctly and you still have a light leave it control is not cheap for an annoying light

your exhaust is clogged

CHECK THAT THE EXHAUST HOSE IS OPEN AND NOT FULL OF LINT OR BLOCKED. OR TAKE HOSE LOOSE FROM BACK AND SEE IF THAT RESOLVES PROBLEM..

You might need to check the exhaust on the rear of the Dryer, or the blower motor iether one has lint inside, restricting the air flow

Make sure the exhaust vent line is not clogged. Check the entire length all the way to the outlet.

Turn off breaker wait an hour turn back on.

The check filter light comes on every load to remind you to clean the lint filter. Cooling only happens when that light is flashing not when it's on solid. If this is a gas dryer check the exhaust hose and vent on the outside of the house. If it is blocked it will not let the unit get to the correct temp due to cycling.