The J310 may not work in an 800MHz oscillator ..
What you need to do is to generate ≈260MHz(160MHz) base frequency with the J310, and then multiply it by3 (5) ..
Here is an example: https://www.qsl.net/yo5ofh/projects/2400mhz_signal/13cm.htm
Depending on your application, a 800Mhz osc can be easily made using a common MMIC amp (MAR series from Minicircuits and others) and resonator. For the resonator you have a wide choice according to stability and noise performance: ceramic, lumped-LC, coax line, microstrip etc.
I can't tell from that schematic. We don't know the inductance of the strip lines.
If there is a mutiplier then it is further down the circuit. The part of the circuit you have shown just contains an oscillator and a buffer amplifer.
There must not be multiplier itslef. If the tank circuit is resonated at 2nd or 3rd harmonic, the oscillator may work lower frequencies.Because every oscillator creates harmonics less or more...
i have seen wheather forecast ballon with one element telemetry transceiver . I did not know the frequency but its output was directly connected to 1/4 grond plane antenna about 8 cm length ~ 32 cm wave length.
may be i am wrong.