So will the fosi Audio V3 not work particularly well with just a phono output from a phone ?
No it's not, why would you say thatNot sure if you realise but they're "mono" amplifiers so you need a pair of them and an appropriate in which case they'd work well .... if you only want a single amp their ZA3 may be a better choice.
I'm guessing you already have speakers or will you be looking for those as well?

No it's not, why would you say that
I think you're alluding to Bluetooth functionality?So would the fosi be good for linking a phone to my tannoys ?
Fosi, amongst some others, do their R&D in the field. This means you, as the punter, are often doing their testing. There are others.
Most people assume 'Bluetooth' for this but you can obviously use one of these sort of things https://www.ebay.co.uk/itm/192947936184, with or without a USB DAC on the phone like https://www.whathifi.com/reviews/ifi-go-link-max , to drive any amp with RCA inputs such as the Fosi.So would the fosi be good for linking a phone to my tannoys ?
