There are a couple of options. In my opinion the best one is to set the matter up as a flat fee. You can record all of your time but the actual time will not be billed only the flat fee value. With the right bill layout you will not show the dollar value of the time. For the work that is being done on an hourly basis record the tone and change it from billable to override. Override acts as an add to flat fee and will add that’s slips billable value to the billing. 
You can also setup the matter as hourly and create both hourly and flat rate slips. However if multiple people contribute to the flat fee or it will be made up if multiple time entries the first method provides better reporting and is easier. 

There are a couple of options. In my opinion the best one is to set the matter up as a flat fee. You can record all of your time but the actual time will not be billed only the flat fee value. With the right bill layout you will not show the dollar value of the time. For the work that is being done on an hourly basis record the tone and change it from billable to override. Override acts as an add to flat fee and will add that’s slips billable value to the billing. 
You can also setup the matter as hourly and create both hourly and flat rate slips. However if multiple people contribute to the flat fee or it will be made up if multiple time entries the first method provides better reporting and is easier.