Several photonic microring resonators (MRRs) based analog accelerators have been proposed to accelerate the inference of integer-quantized CNNs with remarkably higher throughput and energy efficiency compared to their electronic counterparts. However, the existing analog photonic accelerators suffer from three shortcomings: (i) severe hampering of wavelength parallelism due to various crosstalk effects, (ii) inflexibility of supporting various dataflows other than the weight-stationary dataflow, and (iii) failure in fully leveraging the ability of photodetectors to perform in-situ accumulations. These shortcomings collectively hamper the performance and energy efficiency of prior accelerators. To tackle these shortcomings, we present a novel Hybrid timE Amplitude aNalog optical Accelerator, called HEANA. HEANA employs hybrid time-amplitude analog optical multipliers (TAOMs) that increase the flexibility of HEANA to support multiple dataflows. A spectrally hitless arrangement of TAOMs significantly reduces the crosstalk effects, thereby increasing the wavelength parallelism in HEANA. Moreover, HEANA employs our invented balanced photo-charge accumulators (BPCAs) that enable buffer-less, in-situ, temporal accumulations to eliminate the need to use reduction networks in HEANA, relieving it from related latency and energy overheads. Our evaluation for the inference of four modern CNNs indicates that HEANA provides improvements of atleast 66x and 84x in frames-per-second (FPS) and FPS/W (energy-efficiency), respectively, for equal-area comparisons, on gmean over two MRR-based analog CNN accelerators from prior work.