If you want to make simple gifs - try https://ezgif.com/ - a lot of options, optimizing etc.
If you want to build more complex animations - you can use SwishMax. It used to be commercial software, now the company publishing it has ceased its operations, the software is abadonned and can be downloaded and activated for free. It is basically for building flash animations but it also has the options of exporting it to GIF. You can download the program from the Polish distributor website (translate page with Google Translator): http://www.swish.pl/swish_max - do not be afraid to use key generator - it's developed by Swish Company, the developer of software you unlock. The SwishMax generated GIF animations are a bit poorly compressed, you can use https://ezgif.com/ to optimize the file
Welcome to the forum!
Some longer time ago I was using some chalk like brushes for little artworks and used as backgrounds some chalkboard images, since those mostly look more realistic here in this regard. However there are also a bunch of vector based drawn chalkboards available on the net, which you can take a look on as a starting point how those are drawn (take a look through their layers etc.). - Below is such a vector based one you can take a look on.
chalkboard.afdesign
