Can I get a savings account at HSBC if I am on chexsystems?

No!

If you are being reported to ChexSystems, you need to order a consumer report, and begin clearing your name. There are some banks that offer second chance accounts which may be an option for you; however, there are several restrictions. It is best to contact the bank requesting them to remove the risk they placed against you.  It is important to attack this issue at the source.