I have a work phone and a personal phone, both are I phones, is there any way to foward the personal calls/texts to the work phone? If I do this are they stored on the work phone?

If you use the same Apple ID on both phones, you can get the same iMessage on both phones. However, as I recall, SMS messages will only go to the number to which they are sent, not both phones unless your carrier offers some other solution. And yes, if you share an Apple ID and the iMessages go to both phones, they are stored on both phones.

So long as both devices remain powered on and connected to service, you could turn on messages in the cloud and get all of your messages, both iMessage and sms/mms on the work phone.

This is, however, a very bad idea. Do not put any personal data on your work phone. You're opening yourself up to a whole lot of potential trouble if you do.

I agree with KiltedTim. If you put anything on your work phone from your personal device, that gives your employer access to that information. You open yourself up to allowing them to search your personal call history, texts, etc. I understand the desire to get rid of one of the devices to lighten the load, but you open yourself up to problems.