I have a VT6421A-based card, and flashrom doesn't seem to want to detect it; below are my lspci and flashrom logs.

I should mention that the only form of unique identifier on my card is "ST515" on the box (googling this reveals the name Sunweit). The BIOS chip seems to be empty, as the card does not display its RAID menu on boot as it should.

There's more detail about these cards (and a couple more lspci's) on the wiki at https://wiki.flashrom.org/VT6421A
[collin@reimu ~]$ sudo lspci -nnvvvxx -d 1106:3249
02:05.0 RAID bus controller [0104]: VIA Technologies, Inc. VT6421 IDE/SATA Controller [1106:3249] (rev 50)
	Subsystem: VIA Technologies, Inc. VT6421 IDE/SATA Controller [1106:3249]
	Control: I/O+ Mem+ BusMaster+ SpecCycle- MemWINV- VGASnoop- ParErr- Stepping- SERR- FastB2B- DisINTx-
	Status: Cap+ 66MHz- UDF- FastB2B+ ParErr- DEVSEL=medium >TAbort- <TAbort- <MAbort- >SERR- <PERR- INTx-
	Latency: 32
	Interrupt: pin A routed to IRQ 20
	IOMMU group: 7
	Region 0: I/O ports at d150 [size=16]
	Region 1: I/O ports at d140 [size=16]
	Region 2: I/O ports at d130 [size=16]
	Region 3: I/O ports at d120 [size=16]
	Region 4: I/O ports at d100 [size=32]
	Region 5: I/O ports at d000 [size=256]
	Expansion ROM at fea00000 [disabled] [size=64K]
	Capabilities: [e0] Power Management version 2
		Flags: PMEClk- DSI- D1- D2- AuxCurrent=0mA PME(D0-,D1-,D2-,D3hot-,D3cold-)
		Status: D0 NoSoftRst- PME-Enable- DSel=0 DScale=0 PME-
	Kernel driver in use: sata_via
	Kernel modules: sata_via
00: 06 11 49 32 07 00 90 02 50 00 04 01 00 20 00 00
10: 51 d1 00 00 41 d1 00 00 31 d1 00 00 21 d1 00 00
20: 01 d1 00 00 01 d0 00 00 00 00 00 00 06 11 49 32
30: 00 00 a0 fe e0 00 00 00 00 00 00 00 0b 01 00 00

[collin@reimu ~]$ sudo flashrom -p atavia -VVV
flashrom v1.2 on Linux 5.19.3-arch1-1 (x86_64)
flashrom is free software, get the source code at https://flashrom.org

flashrom was built with libpci 3.8.0, GCC 12.1.0, little endian
Command line (3 args): flashrom -p atavia -VVV
Using clock_gettime for delay loops (clk_id: 1, resolution: 1ns).
Initializing atavia programmer
Error: No supported PCI device found.
Error: Programmer initialization failed.