Charging a mobile Tablet while communicating with a USB device at the same time
The mode you are looking for is called "Accessory Charging" mode, introduced in USB OTG, and enhanced in Type-C connector as DRP, "Dual-Role-Power" mode.

If the connector is of micro-USB/mini-USB type, the ID pin should be grounded with 100-125k resistor, which indicates "accessory charger mode". Then, if supported by tablet, the tablet will act as host, but will accept VBUS charging (instead of being a source, as normal USB hosts do). People sell cable gender-changers ("OTG charging cable") to perform this function. Again, it works if the accessory charging mode is supported by tablet/phone, and if the Y-cable is done right, which is not always the case.

If the connector is of Type-C, then things are more complicated. A special combination of pull up/down resistors on two CC wires should put the port into a "sinking host" mode, see Table 4-13 for "power role behavioral mode summary". The power role swap can be implemented at Type-C state machine level, or as a part of Power Delivery protocol. See Section 4.5 of Type-C Specifications, for several available modes for PR (Power Role) swap function.

The FT311 is a "host" chip, and is not suitable for devices. And the problem might be on tablet side, as Chris mentioned, not on device side.