I recently moved and my sister gave me a washer and dryer. It’s a gas dryer and I found out that my basement doesn’t have a gas line. I have a gas line in the kitchen that the stove is using. Is it possible to safely get a splitter and run one hose to the stove and the other to the dryer?
You need to check your local codes. I wouldn't be running any hoses for any great distances. I'd extend the line with galvanized steel or black steel piping and tee off to the stove and dryer with shutoff valves. Many locations do not allow homeowners to install or modify their gas lines. Many gas companies will come out and hook up your new appliances for little or no cost and they'll also check the rest of your installation.
I have a natural gas dryer. I called a gas fitter to run a new line for me. I mentioned that in the future, I want to add a natural gas firepit, bbq, and range . I was told that he had to calculate everything as though I was running at the same time and then install lines to suit that. Also required a manifold to be installed. It cost a lot more to do it this way, instead of just hooking up a new line for the dryer only, but now I'm ready to expand and won't need this all redone.
The best solution would be install a new gas approved pipe or upsize the existing before branching out. I will take a SWAG and say it is currently 1/2 black pipe. Do not use galvanized pipe for gas, it is against code in many areas. Why because of the galvanized coating (zink). Over time pieces will flake off and clog your gas regulators and burner units. I would suggest not mixing galvanized and black iron or where they touch corrosion will possibly be accelerated.
By "splitter" you presumably mean something outside the wall in the kitchen. This should not be done. The gas connection to your range is likely sized for just the range. If you were to install a dryer too, the two appliances would draw gas at an excessive rate when running together.
Despite best intentions, you inevitably will run them together one day, and the gas pressure drop from the higher draw, or draught, or flow, could cause poor combustion in the dryer and unsatisfactory operation of the range.
Doing laundry is important so it is well worth your while to have a proper gas line and exhaust vent installed in your basement and locate the dryer next to the washer. You might spend some time walking around the house to determine where the gas line enters and to assess your options, possibly running the gas plumbing attached to the floor joists. Of course, if you DIY this you should use black iron pipe or flexible yellow gas piping. You might also look for a friendly gas plumber who would be willing to let you do the bulk of the pipe installation labor; let him/her inspect it and perform the final cut-in and water testing for you so you can sleep well at night.
Also you might someday sell the place. Records show no permit was pulled, no contractor did the work. Suppose there's a gas explosion with a fatality even decades from now. Be assured: the next-of-kin will find you.