The CD4508 contains two 4 bit latches with separate output disable pins. When they are high the latch outputs are tristate.
For each input digit use 1/2 4508. Wire the outputs of all the 4508s together, all Q0 in parallel, then separately all Q1 in parallel etc. to form the BCD data bus. Its crucially important (to avoid smoke!) that you only turn on ONE half 4508's outputs at a time so you need a sequential 1 of N active low signal to drive each the OUTPUT DISABLE pins. If you use a 4017 its outputs are active high so you'd need an inverter for each 1/2 4508.
The combined Q0 - Q3 signals then go to the BCD to 7 segment decoder chip which in turn drives your HV segment anode drivers. A CD4055 would be a better choice here because you don't have to drive a latch pin. Its Disp. Freq pin can be tied high or low for inverted or non-inverted output respectievly which may make you HV driver interfacing easier.
Each HV digit grid driver needs to be turned on one at a time by the active 4017 (or other decoded counter) output so the digit is lit at (almost) the same time its segment data is put on the bus and decoded by the 4055.
Ideally, to avoid ghosting, you'll have a master blanking signal to the HV drivers for either the grids or the segments (or use a BCD to 7 segment chip that supports blanking) so your clock logic can turn the current digit off fractionally before it increments the 4017 count and turn it back on for the next digit after the 4055's outputs have had time to settle. That means you need two monostables, one for the blanking pulse and the other to delay the 4017 clock input so it occurs in the middle of the blanking pulse. A CMOS 555 is plenty good enough for the display scan clock source.
See
https://www.noritake-elec.com/technology/general-technical-information/vfd-operation, section 4 for timing details.
Put that all together, and to the rest of your project, the input side of all the 4508 latches is just like driving individual BCD to 7 segment decoders each wired to a single LED digit. Its worth noting that the 4508 doesn't need a strobe, just tie it high and the current input data goes straight to its tri-state output buffers under the control of the DISABLE signal.
Hopefully that gives you enough of an idea to sketch a block diagram - don't worry about the individual data or segment lines yet, just get the control signals right for two digits and their grids and annotate it that you have N-2 more digits the same (assuming your display has 10 or less digits. If its got more, *DON'T* use a 4017 because they are total absolute pigs to cascade for sequential outputs without glitching).